Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
146 conjugacy classes of subgroups; only the 30 normal subgroups are shown.
This group has 146 conjugacy classes of subgroups — too many to draw. Only its 30 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 |
|---|---|---|
| 6. C2×C4⋊Dic181 | C4 | semidirect |
| 10. #95×C181 | C4 | semidirect |
| 69. C181 | #1344 | semidirect |
| 80. #95 | #10624382 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26042157 | 2 |
| #26042123 | 2 |
| #26041206 | 2 |
| #1344 | 181 |