Finite Group DatabasebetaFinite Group DatabasebetaOrder 1472.
258 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 107 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2 | C22×D92 |
| commutator, cosocle | C4×C23 | C24 |
| Frattini | C4 | C23×D23 |
| Fitting | C23×#131 | C2 |
| socle | C2×C23 | C22×D4 |
| hypercenter | #131 | D23 |
| hypocenter | C23 | #577 |
| LCS | G ▷ C4×C23 ▷ C2×C23 ▷ C23 | |
| UCS | C1 ◁ C2 ◁ #41 ◁ #131 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #10625161 | C2 | semidirect |
| 2. #10625160 | C2 | semidirect |
| 3. C23×#131 | C2 | semidirect |
| 4. #10625080 | C2 | semidirect |
| 5. #10625079 | C2 | semidirect |
| 6. #10625075 | C2 | semidirect |
| 7. C2×#67263 | C2 | semidirect |
| 14. #67288 | C22 | semidirect |
| 16. C2×Dic46 | C22 | semidirect |
| 17. M16×C23 | C22 | semidirect |
| 18. C2×C8×C23 | C22 | semidirect |
| 19. Dic92 | C22 | semidirect |
| 20. D184 | C22 | semidirect |
| 21. #67263 | C22 | semidirect |
| 22. #67263 | C22 | semidirect |
| 23. #67263 | C22 | semidirect |
| 60. #131 | D23 | semidirect |
| 61. C23 | #577 | semidirect |
| 76. M16 | C2×D23 | semidirect |
| 77. C2×C8 | C2×D23 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10625161 | 2 |
| #10625160 | 2 |
| C23×#131 | 2 |
| #10625080 | 2 |
| #10625079 | 2 |
| #10625075 | 2 |
| C2×#67263 | 2 |
| #577 | 23 |