Finite Group DatabasebetaFinite Group DatabasebetaOrder 1472.
262 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 262 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 | C4 | C2×D92 |
| commutator, cosocle | C4×C23 | C24 |
| Frattini | C4 | C23×D23 |
| Fitting | C2×M16×C23 | C2 |
| socle | C2×C23 | C22×D4 |
| hypercenter | C2×M16 | D23 |
| hypocenter | C23 | #575 |
| LCS | G ▷ C4×C23 ▷ C2×C23 ▷ C23 | |
| UCS | C1 ◁ C4 ◁ C22×C4 ◁ C2×M16 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#67288 | C2 | semidirect |
| 2. C2×M16×C23 | C2 | semidirect |
| 3. #10625080 | C2 | semidirect |
| 4. #10625079 | C2 | semidirect |
| 5. #10625075 | C2 | semidirect |
| 11. #67288 | C22 | semidirect |
| 12. C2×D92 | C22 | semidirect |
| 14. C2×Dic46 | C22 | semidirect |
| 15. M16×C23 | C22 | semidirect |
| 16. C2×C8×C23 | C22 | semidirect |
| 17. Dic92 | C22 | semidirect |
| 18. D184 | C22 | semidirect |
| 19. #67263 | C22 | semidirect |
| 54. C2×M16 | D23 | semidirect |
| 55. C23 | #575 | semidirect |
| 68. M16 | C2×D23 | semidirect |
| 69. C2×C8 | C2×D23 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#67288 | 2 |
| C2×M16×C23 | 2 |
| #10625080 | 2 |
| #10625079 | 2 |
| #10625075 | 2 |
| #575 | 23 |