Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
598 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 598 conjugacy classes of subgroups — too many to draw. Only its 85 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. #21434555 | C2 | semidirect |
| 3. #21430032 | C2 | semidirect |
| 4. #21422821 | C2 | semidirect |
| 5. #21422693 | C2 | semidirect |
| 6. #21422603 | C2 | semidirect |
| 7. C59×#1300 | C2 | semidirect |
| 191. #1300 | D59 | semidirect |
| 221. C59 | #10090 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21435085 | 2 |
| #21434555 | 2 |
| #21430032 | 2 |
| #21422821 | 2 |
| #21422693 | 2 |
| #21422603 | 2 |
| C59×#1300 | 2 |
| #10090 | 59 |