Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
484 conjugacy classes of subgroups; only the 202 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 202 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 |
|---|---|---|
| 3. #26042286 | C2 | semidirect |
| 4. #26042285 | C2 | semidirect |
| 5. #26042284 | C2 | semidirect |
| 6. #26042283 | C2 | semidirect |
| 17. #19153883 | C22 | semidirect |
| 18. C4⋊#13089685 | C22 | semidirect |
| 101. C181 | #2905 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#15668459 | 2 |
| C2×D181⋊M16 | 2 |
| #26042286 | 2 |
| #26042285 | 2 |
| #26042284 | 2 |
| #26042283 | 2 |
| #117×D181 | 2 |
| #2905 | 181 |