Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
460 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 460 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. #26041951 | C2 | semidirect |
| 2. #26041656 | C2 | semidirect |
| 3. #26041475 | C2 | semidirect |
| 4. C4×D1448 | C2 | semidirect |
| 5. C8×Q8×C181 | C2 | semidirect |
| 38. Q8×C181 | D8 | semidirect |
| 43. C8×C181 | #41 | semidirect |
| 57. C181 | #3391 | semidirect |
| 62. C8×Q8 | D181 | semidirect |
| 90. Q8 | D1448 | semidirect |
| 101. C8 | #15668450 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041951 | 2 |
| #26041656 | 2 |
| #26041475 | 2 |
| C4×D1448 | 2 |
| C8×Q8×C181 | 2 |
| #3391 | 181 |