Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
484 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 133 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×#19153835 | C2 | semidirect |
| 2. #26041933 | C2 | semidirect |
| 3. #26041659 | C2 | semidirect |
| 4. #26041521 | C2 | semidirect |
| 5. #26041484 | C2 | semidirect |
| 6. #26041442 | C2 | semidirect |
| 7. C8×D724 | C2 | semidirect |
| 8. C4×D8×C181 | C2 | semidirect |
| 49. D8×C181 | D4 | semidirect |
| 85. C4×C181 | #135 | semidirect |
| 95. C181 | #3283 | semidirect |
| 103. C4×D8 | D181 | semidirect |
| 137. D8 | D724 | semidirect |
| 183. C4 | #19153835 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153835 | 2 |
| #26041933 | 2 |
| #26041659 | 2 |
| #26041521 | 2 |
| #26041484 | 2 |
| #26041442 | 2 |
| C8×D724 | 2 |
| C4×D8×C181 | 2 |
| #3283 | 181 |