Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
234 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 69 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. #21423713 | C2 | semidirect |
| 4. #21422165 | C2 | semidirect |
| 5. #21422154 | C2 | semidirect |
| 6. #21422153 | C2 | semidirect |
| 49. D8×C59 | Q16 | semidirect |
| 126. C59 | #12447 | semidirect |
| 154. D8 | #11745672 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21426243 | 2 |
| #21423713 | 2 |
| D8×C59⋊C8 | 2 |
| #21422165 | 2 |
| #21422154 | 2 |
| #21422153 | 2 |
| C59×#2226 | 2 |
| #12447 | 59 |