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. #26041944 | C2 | semidirect |
| 3. #26041686 | C2 | semidirect |
| 4. #26041578 | C2 | semidirect |
| 5. #26041568 | C2 | semidirect |
| 6. #26041566 | C2 | semidirect |
| 7. #26041556 | C2 | semidirect |
| 8. #26041409 | C2 | semidirect |
| 11. #498×C181 | C2 | semidirect |
| 50. D1448 | Q8 | semidirect |
| 80. D724 | C2×Q8 | semidirect |
| 98. C8×C181 | C2×Q8 | semidirect |
| 121. C181 | #3384 | semidirect |
| 126. #498 | 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 |
|---|---|
| #26041990 | 2 |
| #26041944 | 2 |
| #26041686 | 2 |
| #26041578 | 2 |
| #26041568 | 2 |
| #26041566 | 2 |
| #26041556 | 2 |
| #26041409 | 2 |
| #26041390 | 2 |
| C4×D1448 | 2 |
| #498×C181 | 2 |
| #3384 | 181 |