Finite Group DatabasebetaFinite Group DatabasebetaOrder 1472.
248 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 95 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D23 |
| commutator, socle, cosocle | C22×C23 | C24 |
| Fitting | C23×#124 | C2 |
| prime radical | #10625108 | C2 |
| hypercenter | #124 | D23 |
| hypocenter | C23 | #551 |
| LCS | G ▷ C22×C23 ▷ C23 | |
| UCS | C1 ◁ C22 ◁ #124 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C23×#124 | C2 | semidirect |
| 2. #10625117 | C2 | semidirect |
| 4. #10625106 | C2 | semidirect |
| 5. #10625054 | C2 | semidirect |
| 6. (C22⋊D23)⋊C4 | C2 | semidirect |
| 7. C22⋊C4×D23 | C2 | semidirect |
| 8. #10625050 | C2 | semidirect |
| 9. #10625043 | C2 | semidirect |
| 11. C2×Q8×C23 | C22 | semidirect |
| 14. C22×Dic23 | C22 | semidirect |
| 18. C22⋊C4×C23 | C22 | semidirect |
| 19. C42×C23 | C22 | semidirect |
| 22. C22⋊Dic23 | C22 | semidirect |
| 26. C4⋊Dic23 | C22 | semidirect |
| 27. Dic23⋊C4 | C22 | semidirect |
| 28. Dic23⋊C4 | C22 | semidirect |
| 29. Dic23⋊C4 | C22 | semidirect |
| 30. C4×Dic23 | C22 | semidirect |
| 70. #124 | D23 | semidirect |
| 78. C23 | #551 | semidirect |
| 80. C2×Q8 | C2×D23 | semidirect |
| 97. C22⋊C4 | C2×D23 | semidirect |
| 99. C42 | C2×D23 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#124 | 2 |
| #10625117 | 2 |
| #10625108 | 2 |
| #10625106 | 2 |
| #10625054 | 2 |
| (C22⋊D23)⋊C4 | 2 |
| C22⋊C4×D23 | 2 |
| #10625050 | 2 |
| #10625043 | 2 |
| #551 | 23 |