Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
256 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 71 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. #21426243 | C2 | semidirect |
| 3. #21423688 | C2 | semidirect |
| 4. #21422160 | C2 | semidirect |
| 5. #21422155 | C2 | semidirect |
| 6. #21422141 | C2 | semidirect |
| 7. C8×D8×C59 | C2 | semidirect |
| 52. D8×C59 | SD16 | semidirect |
| 113. C8×D8 | D59 | semidirect |
| 137. C59 | #12418 | semidirect |
| 171. D8 | #11745660 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21426243 | 2 |
| #21426131 | 2 |
| #21423688 | 2 |
| #21422160 | 2 |
| #21422155 | 2 |
| #21422141 | 2 |
| C8×D8×C59 | 2 |
| #12418 | 59 |