Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
284 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 91 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 |
|---|---|---|
| 3. C2×#15690720 | C2 | semidirect |
| 5. #20260634 | C2 | semidirect |
| 6. #20260497 | C2 | semidirect |
| 7. #340×C97 | C2 | semidirect |
| 16. #15690730 | C4 | semidirect |
| 119. C97 | #1936 | semidirect |
| 126. #340 | D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690732 | 2 |
| C2×#15690730 | 2 |
| C2×#15690720 | 2 |
| #20260636 | 2 |
| #20260634 | 2 |
| #20260497 | 2 |
| #340×C97 | 2 |
| #1936 | 97 |