Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
262 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 262 conjugacy classes of subgroups — too many to draw. Only its 66 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. #26042294 | C2 | semidirect |
| 3. #26042283 | C2 | semidirect |
| 5. #26042162 | C2 | semidirect |
| 6. #26042150 | C2 | semidirect |
| 25. #19153744 | C4 | semidirect |
| 26. #19153743 | C4 | semidirect |
| 27. #19153742 | C4 | semidirect |
| 28. #104×C181 | C4 | semidirect |
| 120. C181 | #1861 | semidirect |
| 149. #104 | #10624382 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26042358 | 2 |
| #26042294 | 2 |
| #26042283 | 2 |
| #26042276 | 2 |
| #26042162 | 2 |
| #26042150 | 2 |
| #104×D181 | 2 |
| #1861 | 181 |