Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
678 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 678 conjugacy classes of subgroups — too many to draw. Only its 105 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. #21435403 | C2 | semidirect |
| 2. #21434546 | C2 | semidirect |
| 3. #21425024 | C2 | semidirect |
| 4. #21425016 | C2 | semidirect |
| 5. #21422592 | C2 | semidirect |
| 6. #21421945 | C2 | semidirect |
| 7. C59×#3205 | C2 | semidirect |
| 132. #11745664 | D8 | semidirect |
| 214. #3205 | D59 | semidirect |
| 251. C59 | #10192 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21435403 | 2 |
| #21434546 | 2 |
| #21425024 | 2 |
| #21425016 | 2 |
| #21422592 | 2 |
| #21421945 | 2 |
| C59×#3205 | 2 |
| #10192 | 59 |