Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
420 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 125 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. #26041934 | C2 | semidirect |
| 2. #26041684 | C2 | semidirect |
| 3. #26041591 | C2 | semidirect |
| 4. #26041559 | C2 | semidirect |
| 5. #26041512 | C2 | semidirect |
| 6. C8×D724 | C2 | semidirect |
| 7. #107×D181 | C2 | semidirect |
| 8. C4×D8×C181 | C2 | semidirect |
| 52. D724 | D8 | semidirect |
| 69. C8×C181 | #41 | semidirect |
| 89. C181 | #3334 | semidirect |
| 96. C4×D8 | D181 | semidirect |
| 159. C8 | #15668449 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041934 | 2 |
| #26041684 | 2 |
| #26041591 | 2 |
| #26041559 | 2 |
| #26041512 | 2 |
| C8×D724 | 2 |
| #107×D181 | 2 |
| C4×D8×C181 | 2 |
| #3334 | 181 |