Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
348 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 348 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 |
|---|---|---|
| 34. Q8×C181 | Q16 | semidirect |
| 50. C181 | #3395 | semidirect |
| 83. Q8 | Dic724 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26042008 | 2 |
| #26041659 | 2 |
| #26041490 | 2 |
| C4×Dic724 | 2 |
| C8×Q8×C181 | 2 |
| #3395 | 181 |