Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
362 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 103 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 |
|---|---|---|
| 2. C2×#19153749 | C2 | semidirect |
| 5. #26041041 | C2 | semidirect |
| 6. #26041034 | C2 | semidirect |
| 7. #389×C181 | C2 | semidirect |
| 18. #19153736 | C4 | semidirect |
| 40. C2×#13089678 | C2×C4 | semidirect |
| 53. C4⋊C4×C181 | C2×C4 | semidirect |
| 66. D724 | C4⋊C4 | semidirect |
| 123. C181 | #1862 | semidirect |
| 129. #389 | D181 | semidirect |
| 176. C4⋊C4 | C4×D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D724 | 2 |
| C2×#19153749 | 2 |
| C2×#19153736 | 2 |
| #26041041 | 2 |
| #26041034 | 2 |
| #389×C181 | 2 |
| #1862 | 181 |