Finite Group DatabasebetaFinite Group DatabasebetaOrder 1472.
268 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 268 conjugacy classes of subgroups — too many to draw. Only its 99 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2 | C2×D4×D23 |
| commutator, cosocle | C4×C23 | C24 |
| Frattini | C4 | C23×D23 |
| Fitting | C2×D8×C23 | C2 |
| socle | C2×C23 | C22×D4 |
| hypercenter | C2×D8 | D23 |
| hypocenter | C23 | #576 |
| LCS | G ▷ C4×C23 ▷ C2×C23 ▷ C23 | |
| UCS | C1 ◁ C2 ◁ C2×C4 ◁ C2×D8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #10625155 | C2 | semidirect |
| 2. C2×D8×C23 | C2 | semidirect |
| 3. #10625103 | C2 | semidirect |
| 4. #10625083 | C2 | semidirect |
| 5. #10625082 | C2 | semidirect |
| 6. D8×D23 | C2 | semidirect |
| 7. #10625075 | C2 | semidirect |
| 8. #10625072 | C2 | semidirect |
| 9. C2×D4×C23 | C22 | semidirect |
| 12. #67290 | C22 | semidirect |
| 14. D4×D23 | C22 | semidirect |
| 16. #67288 | C22 | semidirect |
| 17. D8×C23 | C22 | semidirect |
| 18. D8×C23 | C22 | semidirect |
| 19. C2×C8×C23 | C22 | semidirect |
| 20. #67273 | C22 | semidirect |
| 21. #67272 | C22 | semidirect |
| 22. #67267 | C22 | semidirect |
| 23. Dic92 | C22 | semidirect |
| 24. D184 | C22 | semidirect |
| 25. #67263 | C22 | semidirect |
| 26. #67262 | C22 | semidirect |
| 27. C8×D23 | C22 | semidirect |
| 69. C2×D8 | D23 | semidirect |
| 71. C23 | #576 | semidirect |
| 79. C2×D4 | C2×D23 | semidirect |
| 85. D8 | C2×D23 | semidirect |
| 86. D8 | C2×D23 | semidirect |
| 90. C2×C8 | C2×D23 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10625155 | 2 |
| C2×D8×C23 | 2 |
| #10625103 | 2 |
| #10625083 | 2 |
| #10625082 | 2 |
| D8×D23 | 2 |
| #10625075 | 2 |
| #10625072 | 2 |
| #576 | 23 |