Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
332 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 332 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 |
|---|---|---|
| 11. #19153781 | C4 | semidirect |
| 17. #19153741 | C4 | semidirect |
| 18. #19153739 | C4 | semidirect |
| 57. Dic362 | C42 | semidirect |
| 101. Dic181 | #103 | semidirect |
| 109. C181 | C4×#103 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153781 | 2 |
| C2×#19153741 | 2 |
| C2×#19153739 | 2 |
| C2×C8×Dic181 | 2 |
| C4⋊C4×Dic181 | 2 |
| #26041041 | 2 |
| #340×C181 | 2 |
| C4×#103 | 181 |