Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
534 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 534 conjugacy classes of subgroups — too many to draw. Only its 127 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. #21425084 | C2 | semidirect |
| 4. #21422778 | C2 | semidirect |
| 6. #21422385 | C2 | semidirect |
| 7. C59×#1567 | C2 | semidirect |
| 129. C8×C59 | #100 | semidirect |
| 152. #1567 | D59 | semidirect |
| 179. C59 | #9805 | semidirect |
| 285. C8 | #14273643 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16837775 | 2 |
| #21425084 | 2 |
| #21424935 | 2 |
| #21422778 | 2 |
| #21422765 | 2 |
| #21422385 | 2 |
| C59×#1567 | 2 |
| #9805 | 59 |