Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
338 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 59 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. #21426282 | C2 | semidirect |
| 3. #21426277 | C2 | semidirect |
| 4. #21425536 | C2 | semidirect |
| 5. #21422112 | C2 | semidirect |
| 6. #21422112 | C2 | semidirect |
| 7. C59×#1315 | C2 | semidirect |
| 16. C2×#14273661 | C22 | semidirect |
| 23. #16837167 | C22 | semidirect |
| 25. C59×C22⋊C16 | C22 | semidirect |
| 26. C59×C22⋊C16 | C22 | semidirect |
| 163. #1315 | D59 | semidirect |
| 186. C22⋊C16 | C2×D59 | semidirect |
| 187. C22⋊C16 | C2×D59 | semidirect |
| 190. C59 | #12284 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21434961 | 2 |
| #21426282 | 2 |
| #21426277 | 2 |
| #21425536 | 2 |
| #21422112 | 2 |
| C59×#1315 | 2 |
| #12284 | 59 |