Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
242 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 242 conjugacy classes of subgroups — too many to draw. Only its 85 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 |
|---|---|---|
| 2. #21422902 | C2 | semidirect |
| 4. #21422059 | C2 | semidirect |
| 6. C16×C59⋊C8 | C2 | semidirect |
| 7. C59×#1372 | C2 | semidirect |
| 28. #14273672 | C8 | semidirect |
| 61. Dic236 | C2×C8 | semidirect |
| 66. C16×C59 | C2×C8 | semidirect |
| 88. C59⋊C8 | SD32 | semidirect |
| 105. #1372 | D59 | semidirect |
| 128. C59 | C8×SD32 | semidirect |
| 173. C16 | C8×D59 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14273672 | 2 |
| #21422902 | 2 |
| #21422890 | 2 |
| #21422059 | 2 |
| #21422056 | 2 |
| C16×C59⋊C8 | 2 |
| C59×#1372 | 2 |
| C8×SD32 | 59 |