Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
656 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 656 conjugacy classes of subgroups — too many to draw. Only its 173 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. C2×#19153844 | C2 | semidirect |
| 2. #26041829 | C2 | semidirect |
| 3. C2×#19153813 | C2 | semidirect |
| 4. #26041668 | C2 | semidirect |
| 5. #26041656 | C2 | semidirect |
| 6. #26041652 | C2 | semidirect |
| 7. C4×M16×C181 | C2 | semidirect |
| 12. C2×#15668438 | C22 | semidirect |
| 13. C2×D1448 | C22 | semidirect |
| 14. #19153816 | C22 | semidirect |
| 18. #19153813 | C22 | semidirect |
| 19. #19153804 | C22 | semidirect |
| 24. #97×C181 | C22 | semidirect |
| 25. C4×C8×C181 | C22 | semidirect |
| 45. M16×C181 | D4 | semidirect |
| 71. C8×C181 | C2×D4 | semidirect |
| 82. C4×C181 | AGL(1,ℤ/8) | semidirect |
| 90. C181 | #3151 | semidirect |
| 98. C4×M16 | D181 | semidirect |
| 115. #97 | C2×D181 | semidirect |
| 116. C4×C8 | C2×D181 | semidirect |
| 134. M16 | D724 | semidirect |
| 162. C8 | C2×D724 | semidirect |
| 174. C4 | #19153844 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153844 | 2 |
| #26041829 | 2 |
| C2×#19153813 | 2 |
| #26041668 | 2 |
| #26041656 | 2 |
| #26041652 | 2 |
| C4×M16×C181 | 2 |
| #3151 | 181 |