Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
528 conjugacy classes of subgroups; only the 234 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 234 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. #26042297 | C2 | direct (N × H) |
| 2. C2×#19153883 | C2 | semidirect |
| 4. C2×C4×#13089685 | C2 | semidirect |
| 7. #19153883 | C22 | semidirect |
| 9. C4×#13089685 | C22 | semidirect |
| 27. C2×C4×D181 | C8 | semidirect |
| 56. C4×D181 | C2×C8 | semidirect |
| 79. C2×C181 | #431 | semidirect |
| 84. C181 | C2×#431 | semidirect |
| 165. C2 | #26042297 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26042297 | 2 |
| C2×#19153883 | 2 |
| C2×#19153873 | 2 |
| C2×C4×#13089685 | 2 |
| C2×C42×D181 | 2 |
| C2×#431 | 181 |