Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
586 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 586 conjugacy classes of subgroups — too many to draw. Only its 101 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. C22×#14273668 | C2 | semidirect |
| 2. #21434583 | C2 | semidirect |
| 3. C2×#16837216 | C2 | semidirect |
| 4. C2×#16837209 | C2 | semidirect |
| 5. #21425007 | C2 | semidirect |
| 6. #21422186 | C2 | semidirect |
| 7. C2×C59×#509 | C2 | semidirect |
| 52. C2×C59⋊C16 | D4 | semidirect |
| 73. C2×D8×C59 | D4 | semidirect |
| 78. M32×C59 | D4 | semidirect |
| 200. C2×#509 | D59 | semidirect |
| 237. C59 | #13336 | semidirect |
| 263. C2×D8 | C22⋊D59 | semidirect |
| 276. M32 | C22⋊D59 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14273668 | 2 |
| #21434583 | 2 |
| C2×#16837216 | 2 |
| C2×#16837209 | 2 |
| #21425007 | 2 |
| #21422186 | 2 |
| C2×C59×#509 | 2 |
| #13336 | 59 |