Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
612 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 612 conjugacy classes of subgroups — too many to draw. Only its 83 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. #21422434 | C2 | semidirect |
| 3. #21422125 | C2 | semidirect |
| 4. #21422098 | C2 | semidirect |
| 5. C59×#1800 | C2 | semidirect |
| 206. #1800 | D59 | semidirect |
| 235. C59 | #11828 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21427311 | 2 |
| #21422434 | 2 |
| #21422125 | 2 |
| #21422098 | 2 |
| C59×#1800 | 2 |
| #11828 | 59 |