Finite Group DatabasebetaFinite Group DatabasebetaOrder 14912.
104 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 104 conjugacy classes of subgroups — too many to draw. Only its 45 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. #21418543 | C2 | semidirect |
| 3. #21418542 | C2 | semidirect |
| 4. #21418470 | C2 | semidirect |
| 5. #21418463 | C2 | semidirect |
| 6. #21418446 | C2 | semidirect |
| 7. #104×C233 | C2 | semidirect |
| 9. #16836584 | C4 | semidirect |
| 10. #16836582 | C4 | semidirect |
| 11. #16836581 | C4 | semidirect |
| 12. #16836579 | C4 | semidirect |
| 51. C233 | #444 | semidirect |
| 58. #104 | D233 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21418555 | 2 |
| #21418543 | 2 |
| #21418542 | 2 |
| #21418470 | 2 |
| #21418463 | 2 |
| #21418446 | 2 |
| #104×C233 | 2 |
| #444 | 233 |