Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
1786 conjugacy classes of subgroups; only the 328 normal subgroups are shown.
This group has 1786 conjugacy classes of subgroups — too many to draw. Only its 328 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C24×#3624 | C2 | semidirect |
| 2. C2×#11763836 | C2 | semidirect |
| 3. #14544759 | C2 | semidirect |
| 4. #14544728 | C2 | semidirect |
| 5. #14544606 | C2 | semidirect |
| 6. C22⋊C4×#3624 | C2 | semidirect |
| 8. C22×#63242 | C22 | semidirect |
| 13. C2×#10587544 | C22 | semidirect |
| 14. C2×#10587543 | C22 | semidirect |
| 17. C2×C4×#3624 | C22 | semidirect |
| 18. #11763675 | C22 | semidirect |
| 37. C22×#3624 | D4 | semidirect |
| 45. #10587639 | C8 | semidirect |
| 60. C24×C17 | C2×C8 | semidirect |
| 67. C2×C22⋊D17 | C2×C8 | semidirect |
| 92. C22⋊Dic17 | C2×C8 | semidirect |
| 109. C22×D17 | C22×C8 | semidirect |
| 122. C2×Dic17 | C22×C8 | semidirect |
| 130. #3624 | #120 | semidirect |
| 143. C22×C17 | C8×D4 | semidirect |
| 211. C17 | C8×#120 | semidirect |
| 215. C24 | #63242 | semidirect |
| 292. C22 | #11763836 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×#3624 | 2 |
| C2×#11763836 | 2 |
| #14544759 | 2 |
| #14544728 | 2 |
| #14544606 | 2 |
| C22⋊C4×#3624 | 2 |
| #14531283 | 2 |
| C8×#120 | 17 |