Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
540 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 540 conjugacy classes of subgroups — too many to draw. Only its 101 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. C22×#14273670 | C2 | semidirect |
| 3. C2×#16837218 | C2 | semidirect |
| 4. #21425811 | C2 | semidirect |
| 5. C2×#16837186 | C2 | semidirect |
| 6. #21422191 | C2 | semidirect |
| 7. C59×#3059 | C2 | semidirect |
| 190. #3059 | D59 | semidirect |
| 222. C59 | #13320 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14273670 | 2 |
| C2×#16837672 | 2 |
| C2×#16837218 | 2 |
| #21425811 | 2 |
| C2×#16837186 | 2 |
| #21422191 | 2 |
| C59×#3059 | 2 |
| #13320 | 59 |