Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
438 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 438 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 1. #21433167 | C2 | semidirect |
| 2. #21422801 | C2 | semidirect |
| 3. #21422720 | C2 | semidirect |
| 4. #21422448 | C2 | semidirect |
| 5. C59⋊#1308 | C2 | semidirect |
| 6. #21421959 | C2 | semidirect |
| 192. C59 | #9333 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21433167 | 2 |
| #21422801 | 2 |
| #21422720 | 2 |
| #21422448 | 2 |
| C59⋊#1308 | 2 |
| #21421959 | 2 |
| C59×#3213 | 2 |
| #9333 | 59 |