Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
576 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 576 conjugacy classes of subgroups — too many to draw. Only its 173 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. #20260635 | C2 | semidirect |
| 3. #20260627 | C2 | semidirect |
| 4. #20260618 | C2 | semidirect |
| 5. #20260613 | C2 | semidirect |
| 6. #20260611 | C2 | semidirect |
| 7. #20260609 | C2 | semidirect |
| 8. #20260595 | C2 | semidirect |
| 9. #381×C97 | C2 | semidirect |
| 13. #15690784 | C4 | semidirect |
| 37. C2×C22⋊D97 | C2×C4 | semidirect |
| 45. C4⋊Dic97 | C2×C4 | semidirect |
| 52. #13095488 | C2×C4 | semidirect |
| 56. C22×C4×C97 | C2×C4 | semidirect |
| 130. C97 | #2377 | semidirect |
| 138. #381 | D97 | semidirect |
| 176. C22×C4 | C4×D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690784 | 2 |
| #20260635 | 2 |
| #20260627 | 2 |
| #20260618 | 2 |
| #20260613 | 2 |
| #20260611 | 2 |
| #20260609 | 2 |
| #20260595 | 2 |
| #381×C97 | 2 |
| #2377 | 97 |