Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
1162 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 1162 conjugacy classes of subgroups — too many to draw. Only its 171 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×#16837215 | C2 | semidirect |
| 2. #21425707 | C2 | semidirect |
| 3. #21424134 | C2 | semidirect |
| 5. C2×#14273667 | C22 | semidirect |
| 6. C2×#14273663 | C22 | semidirect |
| 116. C22×C59 | #361 | semidirect |
| 145. C59 | #12736 | semidirect |
| 243. C22 | #16837215 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16837215 | 2 |
| #21425707 | 2 |
| #21424134 | 2 |
| C23×D8×C59 | 2 |
| #12736 | 59 |