Finite Group DatabasebetaFinite Group DatabasebetaOrder 14912.
120 conjugacy classes of subgroups; only the 42 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 42 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. Q8×#11745400 | C2 | semidirect |
| 3. #21418604 | C2 | semidirect |
| 4. #21418598 | C2 | semidirect |
| 6. #21418589 | C2 | semidirect |
| 18. #16836583 | C4 | semidirect |
| 19. #16836582 | C4 | semidirect |
| 20. #16836581 | C4 | semidirect |
| 22. SD16×C233 | C4 | semidirect |
| 31. Dic466 | C2×C4 | semidirect |
| 36. #14272338 | C2×C4 | semidirect |
| 37. Q8×C233 | C2×C4 | semidirect |
| 39. C8×C233 | C2×C4 | semidirect |
| 58. C233 | #440 | semidirect |
| 73. SD16 | #11745400 | semidirect |
| 85. Q8 | C2×#11745400 | semidirect |
| 98. C8 | C2×#11745400 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×#11745400 | 2 |
| D4×#11745400 | 2 |
| #21418604 | 2 |
| #21418598 | 2 |
| #21418597 | 2 |
| #21418589 | 2 |
| SD16×D233 | 2 |
| #440 | 233 |