Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
512 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 512 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 |
|---|---|---|
| 2. #21435247 | C2 | semidirect |
| 4. #21425039 | C2 | semidirect |
| 6. #21421946 | C2 | semidirect |
| 7. C59×#1981 | C2 | semidirect |
| 188. #1981 | D59 | semidirect |
| 220. C59 | #10202 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21435413 | 2 |
| #21435247 | 2 |
| #21434492 | 2 |
| #21425039 | 2 |
| #21422590 | 2 |
| #21421946 | 2 |
| C59×#1981 | 2 |
| #10202 | 59 |