Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
272 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 129 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 |
|---|---|---|
| 13. #19153745 | C4 | semidirect |
| 16. C8×Dic181 | C4 | semidirect |
| 53. #13089678 | C4⋊C4 | semidirect |
| 78. Dic181 | #97 | semidirect |
| 84. C181 | #1770 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153745 | 2 |
| C2×#19153727 | 2 |
| C2×#19153726 | 2 |
| C2×C8×Dic181 | 2 |
| C4×#15668428 | 2 |
| #26041033 | 2 |
| #336×C181 | 2 |
| #1770 | 181 |