Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
888 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 888 conjugacy classes of subgroups — too many to draw. Only its 115 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. #21424924 | C2 | semidirect |
| 3. #21422831 | C2 | semidirect |
| 4. #21422829 | C2 | semidirect |
| 5. C59×#1962 | C2 | semidirect |
| 6. #16838144 | C4 | semidirect |
| 14. #16837426 | C22 | semidirect |
| 21. C59×#423 | C22 | semidirect |
| 23. C43×C59 | C22 | semidirect |
| 164. #1962 | D59 | semidirect |
| 182. #423 | C2×D59 | semidirect |
| 185. C43 | C2×D59 | semidirect |
| 190. C59 | #8530 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21438501 | 2 |
| #21424924 | 2 |
| #21422831 | 2 |
| #21422829 | 2 |
| C59×#1962 | 2 |
| #8530 | 59 |