Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
374 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 374 conjugacy classes of subgroups — too many to draw. Only its 125 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. #26041990 | C2 | semidirect |
| 2. D4×Dic362 | C2 | semidirect |
| 3. #26041686 | C2 | semidirect |
| 4. #26041675 | C2 | semidirect |
| 5. #26041577 | C2 | semidirect |
| 6. #26041568 | C2 | semidirect |
| 7. #26041560 | C2 | semidirect |
| 8. #26041406 | C2 | semidirect |
| 11. #476×C181 | C2 | semidirect |
| 49. #15668434 | Q8 | semidirect |
| 78. D724 | C2×Q8 | semidirect |
| 87. #13089678 | C2×Q8 | semidirect |
| 121. C181 | #3384 | semidirect |
| 129. #476 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041990 | 2 |
| D4×Dic362 | 2 |
| #26041686 | 2 |
| #26041675 | 2 |
| #26041577 | 2 |
| #26041568 | 2 |
| #26041560 | 2 |
| #26041406 | 2 |
| #26041388 | 2 |
| C4×#15668434 | 2 |
| #476×C181 | 2 |
| #3384 | 181 |