Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
220 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 47 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. #26042081 | C2 | semidirect |
| 2. C2×#19153757 | C2 | semidirect |
| 3. #26041546 | C2 | semidirect |
| 4. #26041093 | C2 | semidirect |
| 5. #26041086 | C2 | semidirect |
| 6. #26041064 | C2 | semidirect |
| 7. #509×C181 | C2 | semidirect |
| 17. C2×#15668424 | C22 | semidirect |
| 18. #19153752 | C22 | semidirect |
| 21. C2×D8×C181 | C22 | semidirect |
| 24. M32×C181 | C22 | semidirect |
| 93. C181 | #2192 | semidirect |
| 96. #509 | D181 | semidirect |
| 110. C2×D8 | C2×D181 | semidirect |
| 115. M32 | C2×D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26042081 | 2 |
| C2×#19153757 | 2 |
| #26041546 | 2 |
| #26041093 | 2 |
| #26041086 | 2 |
| #26041064 | 2 |
| #509×C181 | 2 |
| #2192 | 181 |