Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
274 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 274 conjugacy classes of subgroups — too many to draw. Only its 65 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. #21426137 | C2 | semidirect |
| 2. #21426133 | C2 | semidirect |
| 4. #21422902 | C2 | semidirect |
| 5. #21422165 | C2 | semidirect |
| 6. #21422141 | C2 | semidirect |
| 7. C59×#1361 | C2 | semidirect |
| 70. Dic236 | D8 | semidirect |
| 101. C59⋊C8 | SD32 | semidirect |
| 123. #1361 | D59 | semidirect |
| 144. C59 | #12425 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21426137 | 2 |
| #21426133 | 2 |
| #21423710 | 2 |
| #21422902 | 2 |
| #21422165 | 2 |
| #21422141 | 2 |
| C59×#1361 | 2 |
| #12425 | 59 |