Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
240 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 240 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. #21426239 | C2 | semidirect |
| 4. C8×Dic236 | C2 | semidirect |
| 5. #21422150 | C2 | semidirect |
| 7. C59×#1367 | C2 | semidirect |
| 63. Dic236 | SD16 | semidirect |
| 90. C8×C59 | SD32 | semidirect |
| 111. #1367 | D59 | semidirect |
| 133. C59 | #12417 | semidirect |
| 202. C8 | #14273672 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21426239 | 2 |
| #21426137 | 2 |
| #21423688 | 2 |
| C8×Dic236 | 2 |
| #21422150 | 2 |
| #21422143 | 2 |
| C59×#1367 | 2 |
| #12417 | 59 |