Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
478 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 478 conjugacy classes of subgroups — too many to draw. Only its 73 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×#15690838 | C2 | semidirect |
| 2. #20261302 | C2 | semidirect |
| 3. C2×#15690806 | C2 | semidirect |
| 4. C2×#15690736 | C2 | semidirect |
| 5. #20260741 | C2 | semidirect |
| 6. #20260496 | C2 | semidirect |
| 7. C2×#100×C97 | C2 | semidirect |
| 34. C2×Dic194 | D4 | semidirect |
| 40. C2×D388 | D4 | semidirect |
| 41. C2×D388 | D4 | semidirect |
| 50. C4⋊Dic97 | D4 | semidirect |
| 55. C4×Dic97 | D4 | semidirect |
| 67. M16×C97 | D4 | semidirect |
| 139. C97 | #2002 | semidirect |
| 145. C2×#100 | D97 | semidirect |
| 200. M16 | C22⋊D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690838 | 2 |
| #20261302 | 2 |
| C2×#15690806 | 2 |
| C2×#15690736 | 2 |
| #20260741 | 2 |
| #20260496 | 2 |
| C2×#100×C97 | 2 |
| #2002 | 97 |