Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
688 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 688 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 |
|---|---|---|
| 1. #21425274 | C2 | semidirect |
| 2. #21425272 | C2 | semidirect |
| 3. #21425263 | C2 | semidirect |
| 5. C59×#2030 | C2 | semidirect |
| 18. C22×Dic118 | Q8 | semidirect |
| 19. C22×D236 | Q8 | semidirect |
| 21. C22×C4×D59 | Q8 | semidirect |
| 101. #2030 | D59 | semidirect |
| 118. C59 | #32874 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21425274 | 2 |
| #21425272 | 2 |
| #21425263 | 2 |
| #21424013 | 2 |
| C59×#2030 | 2 |
| #32874 | 59 |