Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
420 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 420 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. #26041933 | C2 | semidirect |
| 2. #26041684 | C2 | semidirect |
| 3. #26041593 | C2 | semidirect |
| 4. #26041560 | C2 | semidirect |
| 5. #26041515 | C2 | semidirect |
| 6. C4×D1448 | C2 | semidirect |
| 7. C2×#19153750 | C2 | semidirect |
| 8. C8×D4×C181 | C2 | semidirect |
| 60. D4×C181 | D8 | semidirect |
| 69. C8×C181 | #41 | semidirect |
| 89. C181 | #3334 | semidirect |
| 97. C8×D4 | D181 | semidirect |
| 146. D4 | D1448 | semidirect |
| 159. C8 | #15668448 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041933 | 2 |
| #26041684 | 2 |
| #26041593 | 2 |
| #26041560 | 2 |
| #26041515 | 2 |
| C4×D1448 | 2 |
| C2×#19153750 | 2 |
| C8×D4×C181 | 2 |
| #3334 | 181 |