Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
314 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 314 conjugacy classes of subgroups — too many to draw. Only its 67 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. #21436488 | C2 | semidirect |
| 2. #21426321 | C2 | semidirect |
| 3. #21426137 | C2 | semidirect |
| 5. #21422059 | C2 | semidirect |
| 6. #21422050 | C2 | semidirect |
| 7. C59×#1365 | C2 | semidirect |
| 102. D236 | SD32 | semidirect |
| 134. #1365 | D59 | semidirect |
| 159. C59 | #12342 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21436488 | 2 |
| #21426321 | 2 |
| #21426137 | 2 |
| #21423452 | 2 |
| #21422059 | 2 |
| #21422050 | 2 |
| C59×#1365 | 2 |
| #12342 | 59 |