Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
492 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 85 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. #21425705 | C2 | semidirect |
| 3. #341×D59 | C2 | semidirect |
| 4. #21422112 | C2 | semidirect |
| 5. #21422111 | C2 | semidirect |
| 6. #21422110 | C2 | semidirect |
| 7. C59×#1349 | C2 | semidirect |
| 20. C22⋊(C59⋊C16) | C22 | semidirect |
| 22. #16837167 | C22 | semidirect |
| 25. C59×C22⋊C16 | C22 | semidirect |
| 26. C59×#341 | C22 | semidirect |
| 190. #1349 | D59 | semidirect |
| 214. C22⋊C16 | C2×D59 | semidirect |
| 217. #341 | C2×D59 | semidirect |
| 218. C59 | #11711 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #466×D59 | 2 |
| #21425705 | 2 |
| #341×D59 | 2 |
| #21422112 | 2 |
| #21422111 | 2 |
| #21422110 | 2 |
| C59×#1349 | 2 |
| #11711 | 59 |