Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
454 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 454 conjugacy classes of subgroups — too many to draw. Only its 81 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 |
|---|---|---|
| 3. #21434648 | C2 | semidirect |
| 4. #21422568 | C2 | semidirect |
| 6. #21422453 | C2 | semidirect |
| 7. C59×#1291 | C2 | semidirect |
| 183. #1291 | D59 | semidirect |
| 214. C59 | #10126 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21435288 | 2 |
| #21435109 | 2 |
| #21434648 | 2 |
| #21422568 | 2 |
| #21422514 | 2 |
| #21422453 | 2 |
| C59×#1291 | 2 |
| #10126 | 59 |