Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
334 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 97 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 |
|---|---|---|
| 3. #20260744 | C2 | semidirect |
| 4. #20260642 | C2 | semidirect |
| 5. #20260503 | C2 | semidirect |
| 6. #20260496 | C2 | semidirect |
| 24. #137×C97 | C4 | semidirect |
| 54. C2×Q8×C97 | C2×C4 | semidirect |
| 64. M16×C97 | C2×C4 | semidirect |
| 125. C97 | #1882 | semidirect |
| 136. #137 | Dic97 | semidirect |
| 162. C2×Q8 | C2×Dic97 | semidirect |
| 177. M16 | C2×Dic97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261218 | 2 |
| C2×#15690737 | 2 |
| #20260744 | 2 |
| #20260642 | 2 |
| #20260503 | 2 |
| #20260496 | 2 |
| C2×#137×C97 | 2 |
| #1882 | 97 |