Finite Group DatabasebetaFinite Group DatabasebetaOrder 14912.
196 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 91 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. #21418534 | C2 | semidirect |
| 2. #21418533 | C2 | semidirect |
| 3. #21418530 | C2 | semidirect |
| 4. #21418530 | C2 | semidirect |
| 5. #21418528 | C2 | semidirect |
| 6. #21418528 | C2 | semidirect |
| 7. #21418526 | C2 | semidirect |
| 8. #21418525 | C2 | semidirect |
| 12. #21418514 | C2 | semidirect |
| 13. #21418513 | C2 | semidirect |
| 14. #21418511 | C2 | semidirect |
| 15. C22⋊Q8×C233 | C2 | semidirect |
| 97. C233 | #563 | semidirect |
| 113. C22⋊Q8 | D233 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21418534 | 2 |
| #21418533 | 2 |
| #21418530 | 2 |
| #21418528 | 2 |
| #21418526 | 2 |
| #21418525 | 2 |
| #21418521 | 2 |
| #21418518 | 2 |
| #21418517 | 2 |
| #21418514 | 2 |
| #21418513 | 2 |
| #21418511 | 2 |
| C22⋊Q8×C233 | 2 |
| #563 | 233 |