Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
536 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 536 conjugacy classes of subgroups — too many to draw. Only its 97 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 |
|---|---|---|
| 2. #26041297 | C2 | semidirect |
| 3. #26041295 | C2 | semidirect |
| 4. #26041288 | C2 | semidirect |
| 5. #26041261 | C2 | semidirect |
| 6. #26041252 | C2 | semidirect |
| 7. #419×C181 | C2 | semidirect |
| 13. C2×#15668450 | C4 | semidirect |
| 18. C2×Q8×D181 | C4 | semidirect |
| 146. C181 | #1796 | semidirect |
| 152. #419 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153864 | 2 |
| #26041297 | 2 |
| #26041295 | 2 |
| #26041288 | 2 |
| #26041261 | 2 |
| #26041252 | 2 |
| #419×C181 | 2 |
| #1796 | 181 |