Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
726 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 726 conjugacy classes of subgroups — too many to draw. Only its 111 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. #21424020 | C2 | semidirect |
| 4. #21421948 | C2 | semidirect |
| 5. C59×#2310 | C2 | semidirect |
| 6. C2×#14273716 | C4 | semidirect |
| 11. #16837309 | C4 | semidirect |
| 162. #2310 | D59 | semidirect |
| 188. C59 | #9466 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21427750 | 2 |
| #21424020 | 2 |
| #21422624 | 2 |
| #21421948 | 2 |
| C59×#2310 | 2 |
| #9466 | 59 |