Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
314 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 314 conjugacy classes of subgroups — too many to draw. Only its 59 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 |
|---|---|---|
| 2. #26041652 | C2 | semidirect |
| 3. #26041570 | C2 | semidirect |
| 4. #26041569 | C2 | semidirect |
| 5. #26041022 | C2 | semidirect |
| 6. #26041008 | C2 | semidirect |
| 7. D4⋊C8×C181 | C2 | semidirect |
| 11. #19153816 | C22 | semidirect |
| 19. C4⋊#13089678 | C22 | semidirect |
| 23. C4⋊C8×C181 | C22 | semidirect |
| 24. C4×C8×C181 | C22 | semidirect |
| 65. D724 | SD16 | semidirect |
| 74. D4×C181 | SD16 | semidirect |
| 108. C181 | #1629 | semidirect |
| 116. D4⋊C8 | D181 | semidirect |
| 130. C4⋊C8 | C2×D181 | semidirect |
| 133. C4×C8 | C2×D181 | semidirect |
| 178. D4 | #15668438 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×D724 | 2 |
| #26041652 | 2 |
| #26041570 | 2 |
| #26041569 | 2 |
| #26041022 | 2 |
| #26041008 | 2 |
| D4⋊C8×C181 | 2 |
| #1629 | 181 |