Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
386 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 117 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. #26041995 | C2 | semidirect |
| 2. #26041932 | C2 | semidirect |
| 3. #26041605 | C2 | semidirect |
| 4. #26041599 | C2 | semidirect |
| 5. #26041566 | C2 | semidirect |
| 6. #26041556 | C2 | semidirect |
| 7. #26041533 | C2 | semidirect |
| 8. C4×D1448 | C2 | semidirect |
| 9. #26041358 | C2 | semidirect |
| 10. #26041318 | C2 | semidirect |
| 11. #498×C181 | C2 | semidirect |
| 101. C8×C181 | #41 | semidirect |
| 127. C181 | #3354 | semidirect |
| 131. #498 | D181 | semidirect |
| 229. C8 | #15668450 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041995 | 2 |
| #26041932 | 2 |
| #26041605 | 2 |
| #26041599 | 2 |
| #26041566 | 2 |
| #26041556 | 2 |
| #26041533 | 2 |
| C4×D1448 | 2 |
| #26041358 | 2 |
| #26041318 | 2 |
| #498×C181 | 2 |
| #3354 | 181 |