Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
436 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 436 conjugacy classes of subgroups — too many to draw. Only its 137 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. #26041829 | C2 | semidirect |
| 2. #26041560 | C2 | semidirect |
| 3. #26041515 | C2 | semidirect |
| 4. #26041475 | C2 | semidirect |
| 5. C2×C4⋊C8×C181 | C2 | semidirect |
| 52. C2×C4×C181 | D8 | semidirect |
| 76. C181 | #3245 | semidirect |
| 82. C2×C4⋊C8 | D181 | semidirect |
| 129. C2×C4 | D1448 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041829 | 2 |
| #26041560 | 2 |
| #26041515 | 2 |
| #26041475 | 2 |
| C2×C4⋊C8×C181 | 2 |
| #3245 | 181 |