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. #21426234 | C2 | semidirect |
| 3. #21423688 | C2 | semidirect |
| 4. C8×D472 | C2 | semidirect |
| 5. #21422150 | C2 | semidirect |
| 6. #21422143 | C2 | semidirect |
| 7. C59×#1367 | C2 | semidirect |
| 66. D472 | SD16 | semidirect |
| 93. C8×C59 | D16 | semidirect |
| 116. #1367 | D59 | semidirect |
| 139. C59 | #12416 | semidirect |
| 211. C8 | D944 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21426234 | 2 |
| #21426132 | 2 |
| #21423688 | 2 |
| C8×D472 | 2 |
| #21422150 | 2 |
| #21422143 | 2 |
| C59×#1367 | 2 |
| #12416 | 59 |