Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
242 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 242 conjugacy classes of subgroups — too many to draw. Only its 87 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. #21425927 | C2 | semidirect |
| 3. #21422050 | C2 | semidirect |
| 4. C8×C59⋊C16 | C2 | semidirect |
| 5. C59×#1370 | C2 | semidirect |
| 48. C59⋊C16 | D8 | semidirect |
| 61. C8×C59 | M32 | semidirect |
| 78. #1370 | D59 | semidirect |
| 95. C59 | #12039 | semidirect |
| 142. C8 | #14273666 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21425927 | 2 |
| C8×D472 | 2 |
| #21422050 | 2 |
| C8×C59⋊C16 | 2 |
| C59×#1370 | 2 |
| #12039 | 59 |