Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
1190 conjugacy classes of subgroups; only the 219 normal subgroups are shown.
This group has 1190 conjugacy classes of subgroups — too many to draw. Only its 219 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×#16837776 | C2 | semidirect |
| 2. C2×#16837597 | C2 | semidirect |
| 3. #21423179 | C2 | direct (N × H) |
| 4. C2×#16837151 | C2 | semidirect |
| 5. C2×D4⋊(C59⋊C8) | C2 | semidirect |
| 6. C2×C59×#555 | C2 | semidirect |
| 11. #16837776 | C22 | semidirect |
| 13. #16837597 | C22 | semidirect |
| 17. #16837151 | C22 | semidirect |
| 18. D4⋊(C59⋊C8) | C22 | semidirect |
| 21. C59×#555 | C22 | semidirect |
| 162. C2×#555 | D59 | semidirect |
| 169. C2×C59 | #1624 | semidirect |
| 177. #555 | C2×D59 | semidirect |
| 193. C59 | C2×#1624 | semidirect |
| 330. C2 | #21423179 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16837776 | 2 |
| C2×#16837597 | 2 |
| #21423179 | 2 |
| C2×#16837151 | 2 |
| C2×D4⋊(C59⋊C8) | 2 |
| C2×C59×#555 | 2 |
| C2×#1624 | 59 |