Finite Group DatabasebetaFinite Group DatabasebetaOrder 14912.
216 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 95 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. #21418530 | C2 | semidirect |
| 3. #21418524 | C2 | semidirect |
| 4. #21418521 | C2 | semidirect |
| 5. #21418517 | C2 | semidirect |
| 6. #21418515 | C2 | semidirect |
| 8. Q8×Dic233 | C2 | semidirect |
| 9. #21418497 | C2 | semidirect |
| 10. #21418494 | C2 | semidirect |
| 11. C22⋊Q8×C233 | C2 | semidirect |
| 73. C233 | #542 | semidirect |
| 81. 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 |
| #21418530 | 2 |
| #21418524 | 2 |
| #21418521 | 2 |
| #21418517 | 2 |
| #21418515 | 2 |
| #21418509 | 2 |
| Q8×Dic233 | 2 |
| #21418497 | 2 |
| #21418494 | 2 |
| C22⋊Q8×C233 | 2 |
| #542 | 233 |