Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
356 conjugacy classes of subgroups; only the 166 normal subgroups are shown.
This group has 356 conjugacy classes of subgroups — too many to draw. Only its 166 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. #26042330 | C2 | semidirect |
| 2. #26042329 | C2 | semidirect |
| 3. #26042328 | C2 | semidirect |
| 31. #15668459 | Q8 | semidirect |
| 90. C181 | #2962 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26042330 | 2 |
| #26042329 | 2 |
| #26042328 | 2 |
| #26042286 | 2 |
| D181⋊(C4⋊C8) | 2 |
| #26042244 | 2 |
| C4×#15668459 | 2 |
| #26041834 | 2 |
| #2962 | 181 |