Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
468 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 468 conjugacy classes of subgroups — too many to draw. Only its 133 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. C2×#15690841 | C2 | semidirect |
| 3. C22×#13095498 | C2 | semidirect |
| 4. C2×#15690818 | C2 | semidirect |
| 5. #20261001 | C2 | direct (N × H) |
| 6. C2×#15690745 | C2 | semidirect |
| 7. C2×#15690726 | C2 | semidirect |
| 8. C2×#101×C97 | C2 | semidirect |
| 12. #15690841 | C22 | semidirect |
| 21. C2×#13095498 | C22 | semidirect |
| 24. #15690818 | C22 | semidirect |
| 29. #15690745 | C22 | semidirect |
| 30. #15690726 | C22 | semidirect |
| 34. #101×C97 | C22 | semidirect |
| 134. C2×C97 | #471 | semidirect |
| 139. C97 | C2×#471 | semidirect |
| 146. C2×#101 | D97 | semidirect |
| 172. #101 | C2×D97 | semidirect |
| 275. C2 | #20261001 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690841 | 2 |
| C2×#15690838 | 2 |
| C22×#13095498 | 2 |
| C2×#15690818 | 2 |
| #20261001 | 2 |
| C2×#15690745 | 2 |
| C2×#15690726 | 2 |
| C2×#101×C97 | 2 |
| C2×#471 | 97 |