Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
682 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 682 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. #21425086 | C2 | semidirect |
| 3. #21422833 | C2 | semidirect |
| 4. #21422690 | C2 | semidirect |
| 7. C59×#1997 | C2 | semidirect |
| 217. #1997 | D59 | semidirect |
| 254. C59 | #8474 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21437980 | 2 |
| #21425086 | 2 |
| #21422833 | 2 |
| #21422690 | 2 |
| #21422536 | 2 |
| #21422533 | 2 |
| C59×#1997 | 2 |
| #8474 | 59 |