Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
142 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 142 conjugacy classes of subgroups — too many to draw. Only its 49 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. #20261139 | C2 | semidirect |
| 3. #20260560 | C2 | semidirect |
| 4. #20260553 | C2 | semidirect |
| 7. #366×C97 | C2 | semidirect |
| 23. D776 | Q8 | semidirect |
| 64. C97 | #2224 | semidirect |
| 68. #366 | D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261139 | 2 |
| #20260817 | 2 |
| #20260560 | 2 |
| #20260553 | 2 |
| #20260537 | 2 |
| #20260535 | 2 |
| #366×C97 | 2 |
| #2224 | 97 |