Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
324 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 123 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 |
|---|---|---|
| 42. Dic724 | Q8 | semidirect |
| 102. C181 | #3383 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26042006 | 2 |
| #26041683 | 2 |
| #26041680 | 2 |
| #26041589 | 2 |
| #26041583 | 2 |
| #26041563 | 2 |
| C8×Dic362 | 2 |
| C4×Dic724 | 2 |
| #26041373 | 2 |
| #499×C181 | 2 |
| #3383 | 181 |