Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
332 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 84 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. C2×C22⋊#13089685 | C2 | semidirect |
| 2. #26042125 | C2 | semidirect |
| 3. #26042123 | C2 | semidirect |
| 22. C2×C22⋊D181 | C8 | semidirect |
| 45. C22×D181 | C2×C8 | semidirect |
| 55. C2×Dic181 | C2×C8 | semidirect |
| 97. C181 | #1459 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C22⋊#13089685 | 2 |
| #26042125 | 2 |
| #26042123 | 2 |
| C2×#19153776 | 2 |
| #1459 | 181 |