Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
184 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 109 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 |
|---|---|---|
| 4. #20260511 | C2 | semidirect |
| 5. #20260510 | C2 | semidirect |
| 6. C16×Dic97 | C2 | semidirect |
| 7. C4×C16×C97 | C2 | semidirect |
| 11. #15690749 | C4 | semidirect |
| 14. C16×D97 | C4 | semidirect |
| 61. C97 | #2108 | semidirect |
| 68. C4×C16 | D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690749 | 2 |
| C2×C16×D97 | 2 |
| #20260689 | 2 |
| #20260511 | 2 |
| #20260510 | 2 |
| C16×Dic97 | 2 |
| C4×C16×C97 | 2 |
| #2108 | 97 |