Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
476 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 476 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 |
|---|---|---|
| 2. #21426015 | C2 | semidirect |
| 3. #21425106 | C2 | semidirect |
| 4. #21422106 | C2 | semidirect |
| 5. C59×#1314 | C2 | semidirect |
| 6. C22×Dic236 | C22 | semidirect |
| 16. #16837165 | C22 | semidirect |
| 18. C59×C22⋊C16 | C22 | semidirect |
| 94. C23×C59 | SD32 | semidirect |
| 155. #1314 | D59 | semidirect |
| 174. C22⋊C16 | C2×D59 | semidirect |
| 176. C59 | #12105 | semidirect |
| 256. C23 | #14273672 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21434847 | 2 |
| #21426015 | 2 |
| #21425106 | 2 |
| #21422106 | 2 |
| C59×#1314 | 2 |
| #12105 | 59 |