Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
636 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 636 conjugacy classes of subgroups — too many to draw. Only its 99 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. #21434541 | C2 | semidirect |
| 2. #21434097 | C2 | semidirect |
| 3. #21434092 | C2 | semidirect |
| 4. #21424893 | C2 | semidirect |
| 5. #21422494 | C2 | semidirect |
| 6. #21421926 | C2 | semidirect |
| 7. C59×#1480 | C2 | semidirect |
| 140. C2×C59⋊C8 | D8 | semidirect |
| 220. #1480 | D59 | semidirect |
| 254. C59 | #10032 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21434541 | 2 |
| #21434097 | 2 |
| #21434092 | 2 |
| #21424893 | 2 |
| #21422494 | 2 |
| #21421926 | 2 |
| C59×#1480 | 2 |
| #10032 | 59 |