Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
594 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 594 conjugacy classes of subgroups — too many to draw. Only its 131 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. C2×#16837128 | C2 | semidirect |
| 2. #21422030 | C2 | semidirect |
| 3. #21422028 | C2 | semidirect |
| 23. C2×#41×C59 | C8 | semidirect |
| 50. C2×Q8×C59 | C2×C8 | semidirect |
| 57. C2×D4×C59 | C2×C8 | semidirect |
| 175. C59 | #11432 | semidirect |
| 179. C2×#41 | C59⋊C8 | semidirect |
| 209. C2×Q8 | C2×C59⋊C8 | semidirect |
| 216. C2×D4 | C2×C59⋊C8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16837128 | 2 |
| #21422030 | 2 |
| #21422028 | 2 |
| C59×#2311 | 2 |
| #11432 | 59 |