Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
384 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 141 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. #26041575 | C2 | semidirect |
| 5. #26041490 | C2 | semidirect |
| 7. C4×Dic724 | C2 | semidirect |
| 77. C2×C4×C181 | Q16 | semidirect |
| 103. C181 | #3104 | semidirect |
| 181. C2×C4 | Dic724 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041836 | 2 |
| C2×C4×Dic362 | 2 |
| #26041615 | 2 |
| #26041575 | 2 |
| #26041490 | 2 |
| #26041437 | 2 |
| C4×Dic724 | 2 |
| #431×C181 | 2 |
| #3104 | 181 |