Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
388 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 141 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. #26041986 | C2 | semidirect |
| 3. #26041677 | C2 | semidirect |
| 4. #26041610 | C2 | semidirect |
| 5. #26041598 | C2 | semidirect |
| 6. #26041570 | C2 | semidirect |
| 7. #26041565 | C2 | semidirect |
| 8. #26041508 | C2 | semidirect |
| 9. C4×#15668438 | C2 | semidirect |
| 10. C2×#19153748 | C2 | semidirect |
| 11. C8×D4×C181 | C2 | semidirect |
| 91. D4×C181 | SD16 | semidirect |
| 100. C8×C181 | #41 | semidirect |
| 123. C181 | #3335 | semidirect |
| 134. C8×D4 | D181 | semidirect |
| 207. D4 | #15668438 | semidirect |
| 224. C8 | #15668448 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041986 | 2 |
| #26041933 | 2 |
| #26041677 | 2 |
| #26041610 | 2 |
| #26041598 | 2 |
| #26041570 | 2 |
| #26041565 | 2 |
| #26041508 | 2 |
| C4×#15668438 | 2 |
| C2×#19153748 | 2 |
| C8×D4×C181 | 2 |
| #3335 | 181 |