Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
374 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 374 conjugacy classes of subgroups — too many to draw. Only its 133 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. #26041989 | C2 | semidirect |
| 2. Q8×D724 | C2 | semidirect |
| 3. #26041688 | C2 | semidirect |
| 4. #26041677 | C2 | semidirect |
| 5. #26041580 | C2 | semidirect |
| 6. #26041570 | C2 | semidirect |
| 7. #26041570 | C2 | semidirect |
| 8. #26041560 | C2 | semidirect |
| 11. #446×C181 | C2 | semidirect |
| 51. D1448 | Q8 | semidirect |
| 81. D724 | C2×Q8 | semidirect |
| 98. C8×C181 | C2×Q8 | semidirect |
| 121. C181 | #3384 | semidirect |
| 131. #446 | D181 | semidirect |
| 220. C8 | Q8×D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041989 | 2 |
| Q8×D724 | 2 |
| #26041688 | 2 |
| #26041677 | 2 |
| #26041580 | 2 |
| #26041570 | 2 |
| #26041560 | 2 |
| #26041392 | 2 |
| C4×D1448 | 2 |
| #446×C181 | 2 |
| #3384 | 181 |