Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
398 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 95 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. #21426346 | C2 | semidirect |
| 2. #21426345 | C2 | semidirect |
| 3. #21423710 | C2 | semidirect |
| 4. C16×C59⋊C8 | C2 | semidirect |
| 5. C59×#2246 | C2 | semidirect |
| 42. C16×C59 | D8 | semidirect |
| 43. C59⋊C16 | D8 | semidirect |
| 56. C59⋊C8 | D16 | semidirect |
| 68. #2246 | D59 | semidirect |
| 84. C59 | #12515 | semidirect |
| 113. C16 | #11745669 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21426346 | 2 |
| #21426345 | 2 |
| #21423710 | 2 |
| C16×C59⋊C8 | 2 |
| C59×#2246 | 2 |
| #12515 | 59 |