Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
642 conjugacy classes of subgroups; only the 215 normal subgroups are shown.
This group has 642 conjugacy classes of subgroups — too many to draw. Only its 215 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. #21424816 | C2 | semidirect |
| 4. #21424657 | C2 | semidirect |
| 6. #21424239 | C2 | semidirect |
| 7. C59×#1842 | C2 | semidirect |
| 65. C42×C59 | M16 | semidirect |
| 120. #1842 | D59 | semidirect |
| 143. C59 | #23378 | semidirect |
| 194. C42 | #11745659 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14273721 | 2 |
| #21424816 | 2 |
| #21424708 | 2 |
| #21424657 | 2 |
| #21424277 | 2 |
| #21424239 | 2 |
| C59×#1842 | 2 |
| #23378 | 59 |