Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
484 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 131 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×#15690839 | C2 | semidirect |
| 3. C4×Q8×D97 | C2 | semidirect |
| 4. #20260956 | C2 | semidirect |
| 5. #20260955 | C2 | semidirect |
| 6. #20260946 | C2 | semidirect |
| 7. #20260945 | C2 | semidirect |
| 8. #20260932 | C2 | semidirect |
| 9. #20260757 | C2 | semidirect |
| 10. #20260733 | C2 | semidirect |
| 11. #460×C97 | C2 | semidirect |
| 50. Q8×D97 | D4 | semidirect |
| 132. C4×C97 | #137 | semidirect |
| 147. C97 | #3037 | semidirect |
| 156. #460 | D97 | semidirect |
| 285. C4 | #15690839 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690839 | 2 |
| #20261283 | 2 |
| C4×Q8×D97 | 2 |
| #20260956 | 2 |
| #20260955 | 2 |
| #20260946 | 2 |
| #20260945 | 2 |
| #20260932 | 2 |
| #20260757 | 2 |
| #20260733 | 2 |
| #460×C97 | 2 |
| #3037 | 97 |