Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
676 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 676 conjugacy classes of subgroups — too many to draw. Only its 107 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. #21425077 | C2 | semidirect |
| 3. #21422827 | C2 | semidirect |
| 5. #21422733 | C2 | semidirect |
| 6. #21422607 | C2 | semidirect |
| 12. #16838122 | C4 | semidirect |
| 14. D4×Dic118 | C4 | semidirect |
| 239. C59 | #8496 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21438510 | 2 |
| #21425077 | 2 |
| #21422827 | 2 |
| #21422818 | 2 |
| #21422733 | 2 |
| #21422607 | 2 |
| C59×#1505 | 2 |
| #8496 | 59 |