Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
344 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 344 conjugacy classes of subgroups — too many to draw. Only its 79 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. #26042045 | C2 | semidirect |
| 3. #26041284 | C2 | semidirect |
| 4. #26041252 | C2 | semidirect |
| 5. #26041036 | C2 | semidirect |
| 6. #26041035 | C2 | semidirect |
| 7. #418×C181 | C2 | semidirect |
| 13. #19153812 | C4 | semidirect |
| 14. #19153803 | C4 | semidirect |
| 37. C2×#13089678 | D4 | semidirect |
| 56. C2×C8×C181 | D4 | semidirect |
| 115. C181 | #1910 | semidirect |
| 120. #418 | D181 | semidirect |
| 165. C2×C8 | C22⋊D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26042045 | 2 |
| #26041846 | 2 |
| #26041284 | 2 |
| #26041252 | 2 |
| #26041036 | 2 |
| #26041035 | 2 |
| #418×C181 | 2 |
| #1910 | 181 |