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. #26041930 | C2 | semidirect |
| 2. #26041683 | C2 | semidirect |
| 3. #26041594 | C2 | semidirect |
| 4. #26041592 | C2 | semidirect |
| 5. #26041558 | C2 | semidirect |
| 6. #26041516 | C2 | semidirect |
| 7. #26041515 | C2 | semidirect |
| 8. #26041361 | C2 | semidirect |
| 9. C8×C22⋊D181 | C2 | semidirect |
| 10. #107×D181 | C2 | semidirect |
| 11. C2×#107×C181 | C2 | semidirect |
| 77. C22⋊D181 | D8 | semidirect |
| 97. C8×C181 | #41 | semidirect |
| 123. C181 | #3334 | semidirect |
| 135. C2×#107 | D181 | semidirect |
| 221. C8 | #15668449 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041930 | 2 |
| #26041683 | 2 |
| #26041594 | 2 |
| #26041592 | 2 |
| #26041558 | 2 |
| #26041516 | 2 |
| #26041515 | 2 |
| #26041361 | 2 |
| C8×C22⋊D181 | 2 |
| #107×D181 | 2 |
| C2×#107×C181 | 2 |
| #3334 | 181 |