Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
312 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 312 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 |
|---|---|---|
| 2. C4⋊C16×D59 | C2 | semidirect |
| 3. #21422856 | C2 | semidirect |
| 4. #21422149 | C2 | semidirect |
| 5. #21422147 | C2 | semidirect |
| 6. #21422139 | C2 | semidirect |
| 7. C59×#1360 | C2 | semidirect |
| 151. #1360 | D59 | semidirect |
| 176. C59 | #11978 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21434663 | 2 |
| C4⋊C16×D59 | 2 |
| #21422856 | 2 |
| #21422149 | 2 |
| #21422147 | 2 |
| #21422139 | 2 |
| C59×#1360 | 2 |
| #11978 | 59 |