Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
500 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 197 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×#19153822 | C2 | semidirect |
| 3. #26041358 | C2 | semidirect |
| 4. C8×D724 | C2 | semidirect |
| 5. #26041303 | C2 | semidirect |
| 6. #26041245 | C2 | semidirect |
| 7. C2×C4×C8×C181 | C2 | semidirect |
| 41. C2×C8×C181 | D4 | semidirect |
| 75. C4×C181 | #131 | semidirect |
| 83. C181 | #2931 | semidirect |
| 91. C2×C4×C8 | D181 | semidirect |
| 123. C2×C8 | D724 | semidirect |
| 160. C4 | #19153822 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153822 | 2 |
| #26041829 | 2 |
| #26041358 | 2 |
| C8×D724 | 2 |
| #26041303 | 2 |
| #26041245 | 2 |
| C2×C4×C8×C181 | 2 |
| #2931 | 181 |