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. Q16×C59⋊C8 | C2 | semidirect |
| 4. #21422169 | C2 | semidirect |
| 6. C16×C59⋊C8 | C2 | semidirect |
| 7. C59×#1332 | C2 | semidirect |
| 26. #14273670 | C8 | semidirect |
| 48. Q16×C59 | C2×C8 | semidirect |
| 67. C59⋊C16 | C2×C8 | semidirect |
| 88. C59⋊C8 | SD32 | semidirect |
| 106. #1332 | D59 | semidirect |
| 128. C59 | C8×SD32 | semidirect |
| 154. Q16 | C8×D59 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14273670 | 2 |
| Q16×C59⋊C8 | 2 |
| #21422890 | 2 |
| #21422169 | 2 |
| #21422058 | 2 |
| C16×C59⋊C8 | 2 |
| C59×#1332 | 2 |
| C8×SD32 | 59 |