Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
828 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 828 conjugacy classes of subgroups — too many to draw. Only its 131 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. C2×#16837594 | C2 | semidirect |
| 2. #21429012 | C2 | semidirect |
| 3. C2×#16837131 | C2 | semidirect |
| 4. #21421979 | C2 | semidirect |
| 5. C59×#1957 | C2 | semidirect |
| 37. C4⋊(C59⋊C8) | D4 | semidirect |
| 45. #127×C59 | D4 | semidirect |
| 74. C2×D236 | D8 | semidirect |
| 172. #1957 | D59 | semidirect |
| 196. C59 | #10228 | semidirect |
| 209. #127 | D236 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16837594 | 2 |
| #21429012 | 2 |
| C2×#16837131 | 2 |
| #21421979 | 2 |
| C59×#1957 | 2 |
| #10228 | 59 |