Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
264 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 85 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. C2×#15690745 | C2 | semidirect |
| 3. C2×#15690743 | C2 | semidirect |
| 6. #20260503 | C2 | semidirect |
| 7. #343×C97 | C2 | semidirect |
| 10. #15690818 | C4 | semidirect |
| 104. C97 | #1816 | semidirect |
| 111. #343 | D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690818 | 2 |
| C2×#15690745 | 2 |
| C2×#15690743 | 2 |
| #20260737 | 2 |
| #20260734 | 2 |
| #20260503 | 2 |
| #343×C97 | 2 |
| #1816 | 97 |