Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
540 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 540 conjugacy classes of subgroups — too many to draw. Only its 79 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. #21434499 | C2 | semidirect |
| 3. #21429965 | C2 | semidirect |
| 4. #21422644 | C2 | semidirect |
| 5. #21422538 | C2 | semidirect |
| 6. #21421962 | C2 | semidirect |
| 7. C59×#1534 | C2 | semidirect |
| 200. #1534 | D59 | semidirect |
| 235. C59 | #10019 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21434499 | 2 |
| #21434188 | 2 |
| #21429965 | 2 |
| #21422644 | 2 |
| #21422538 | 2 |
| #21421962 | 2 |
| C59×#1534 | 2 |
| #10019 | 59 |