Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
512 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 213 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. #20260634 | C2 | semidirect |
| 3. #20260628 | C2 | semidirect |
| 4. #20260628 | C2 | semidirect |
| 5. #20260621 | C2 | semidirect |
| 7. #20260610 | C2 | semidirect |
| 8. #20260595 | C2 | semidirect |
| 28. #123×C97 | C4 | semidirect |
| 55. C22×C4×C97 | C2×C4 | semidirect |
| 59. C4⋊C4×C97 | C2×C4 | semidirect |
| 61. C22⋊C4×C97 | C2×C4 | semidirect |
| 127. C97 | #2376 | semidirect |
| 140. #123 | Dic97 | semidirect |
| 172. C22×C4 | C2×Dic97 | semidirect |
| 180. C4⋊C4 | C2×Dic97 | semidirect |
| 186. C22⋊C4 | C2×Dic97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20260638 | 2 |
| #20260634 | 2 |
| #20260628 | 2 |
| #20260621 | 2 |
| #20260615 | 2 |
| #20260610 | 2 |
| #20260595 | 2 |
| C2×#123×C97 | 2 |
| #2376 | 97 |