Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
662 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 662 conjugacy classes of subgroups — too many to draw. Only its 81 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. #21434560 | C2 | semidirect |
| 2. #21434187 | C2 | semidirect |
| 3. #21422720 | C2 | semidirect |
| 4. #21422642 | C2 | semidirect |
| 5. #21422539 | C2 | semidirect |
| 6. #21421960 | C2 | semidirect |
| 7. C59×#2631 | C2 | semidirect |
| 42. #14273727 | D4 | semidirect |
| 43. #14273724 | D4 | semidirect |
| 58. #14273638 | D4 | semidirect |
| 59. C4×C59⋊C8 | D4 | semidirect |
| 223. #2631 | D59 | semidirect |
| 260. C59 | #10018 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21434560 | 2 |
| #21434187 | 2 |
| #21422720 | 2 |
| #21422642 | 2 |
| #21422539 | 2 |
| #21421960 | 2 |
| C59×#2631 | 2 |
| #10018 | 59 |