Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
356 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 356 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 |
|---|---|---|
| 2. #26041683 | C2 | semidirect |
| 3. #26041616 | C2 | semidirect |
| 4. #26041614 | C2 | semidirect |
| 5. #26041573 | C2 | semidirect |
| 6. #26041521 | C2 | semidirect |
| 7. #26041520 | C2 | semidirect |
| 8. #26041373 | C2 | semidirect |
| 10. #107×D181 | C2 | semidirect |
| 11. C2×#107×C181 | C2 | semidirect |
| 73. C22⋊D181 | Q16 | semidirect |
| 116. C181 | #3338 | semidirect |
| 128. C2×#107 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041984 | 2 |
| #26041683 | 2 |
| #26041616 | 2 |
| #26041614 | 2 |
| #26041573 | 2 |
| #26041521 | 2 |
| #26041520 | 2 |
| #26041373 | 2 |
| C8×C22⋊D181 | 2 |
| #107×D181 | 2 |
| C2×#107×C181 | 2 |
| #3338 | 181 |