Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
410 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 410 conjugacy classes of subgroups — too many to draw. Only its 137 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. #26041620 | C2 | semidirect |
| 3. #26041614 | C2 | semidirect |
| 4. #26041609 | C2 | semidirect |
| 5. #26041322 | C2 | semidirect |
| 6. #26041287 | C2 | semidirect |
| 18. #19153749 | C22 | semidirect |
| 19. #19153747 | C22 | semidirect |
| 20. #19153739 | C22 | semidirect |
| 21. #19153739 | C22 | semidirect |
| 116. C181 | #3095 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153795 | 2 |
| #26041620 | 2 |
| #26041614 | 2 |
| #26041609 | 2 |
| #26041322 | 2 |
| #26041287 | 2 |
| #26041243 | 2 |
| C2×#117×C181 | 2 |
| #3095 | 181 |