Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
232 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 58 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. #20261746 | C2 | semidirect |
| 4. #20261701 | C2 | semidirect |
| 5. #20261614 | C2 | semidirect |
| 6. #20261610 | C2 | semidirect |
| 23. #15690727 | C4 | semidirect |
| 24. #15690726 | C4 | semidirect |
| 25. #15690726 | C4 | semidirect |
| 26. #100×C97 | C4 | semidirect |
| 115. C97 | #1931 | semidirect |
| 139. #100 | #87604 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261746 | 2 |
| #20261727 | 2 |
| C2×#15690872 | 2 |
| #20261701 | 2 |
| #20261614 | 2 |
| #20261610 | 2 |
| #100×D97 | 2 |
| #1931 | 97 |