Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
610 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 610 conjugacy classes of subgroups — too many to draw. Only its 103 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. #21429092 | C2 | semidirect |
| 3. #21422768 | C2 | semidirect |
| 4. #21422591 | C2 | semidirect |
| 5. #21422486 | C2 | semidirect |
| 6. #21421998 | C2 | semidirect |
| 7. C59×#3226 | C2 | semidirect |
| 215. #3226 | D59 | semidirect |
| 252. C59 | #10239 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21433556 | 2 |
| #21429092 | 2 |
| #21422768 | 2 |
| #21422591 | 2 |
| #21422486 | 2 |
| #21421998 | 2 |
| C59×#3226 | 2 |
| #10239 | 59 |