Finite Group DatabasebetaFinite Group DatabasebetaOrder 14912.
104 conjugacy classes of subgroups; only the 40 normal subgroups are shown.
This group has 104 conjugacy classes of subgroups — too many to draw. Only its 40 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. #21418623 | C2 | semidirect |
| 2. #21418622 | C2 | semidirect |
| 3. #21418606 | C2 | semidirect |
| 4. #21418600 | C2 | semidirect |
| 5. #21418599 | C2 | semidirect |
| 6. #21418589 | C2 | semidirect |
| 18. #16836584 | C4 | semidirect |
| 19. #16836583 | C4 | semidirect |
| 20. #16836579 | C4 | semidirect |
| 22. SD16×C233 | C4 | semidirect |
| 51. C233 | #444 | semidirect |
| 64. SD16 | #11745400 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21418623 | 2 |
| #21418622 | 2 |
| #21418606 | 2 |
| #21418600 | 2 |
| #21418599 | 2 |
| #21418589 | 2 |
| #21418556 | 2 |
| #444 | 233 |