Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
2022 conjugacy classes of subgroups; only the 587 normal subgroups are shown.
This group has 2022 conjugacy classes of subgroups — too many to draw. Only its 587 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. #21432287 | C2 | direct (N × H) |
| 2. C2×#16837344 | C2 | semidirect |
| 4. C2×#16837321 | C2 | semidirect |
| 11. #16837344 | C22 | semidirect |
| 13. #16837321 | C22 | semidirect |
| 114. C2×C59 | #2835 | semidirect |
| 133. C59 | C2×#2835 | semidirect |
| 219. C2 | #21432287 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21432287 | 2 |
| C2×#16837344 | 2 |
| C2×#16837327 | 2 |
| C2×#16837321 | 2 |
| C2×#16837274 | 2 |
| C2×C59×#393 | 2 |
| C2×#2835 | 59 |