Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
284 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 79 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 |
|---|---|---|
| 2. #20260771 | C2 | semidirect |
| 3. #20260753 | C2 | semidirect |
| 4. #20260752 | C2 | semidirect |
| 5. #20260708 | C2 | semidirect |
| 6. #20260691 | C2 | semidirect |
| 7. #410×C97 | C2 | semidirect |
| 13. C2×#13095501 | C4 | semidirect |
| 14. C2×#13095499 | C4 | semidirect |
| 15. C2×#13095498 | C4 | semidirect |
| 16. C2×#13095496 | C4 | semidirect |
| 133. C97 | #1976 | semidirect |
| 139. #410 | D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690830 | 2 |
| #20260771 | 2 |
| #20260753 | 2 |
| #20260752 | 2 |
| #20260708 | 2 |
| #20260691 | 2 |
| #410×C97 | 2 |
| #1976 | 97 |