Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
376 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 91 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. #21424142 | C2 | semidirect |
| 3. #21422085 | C2 | semidirect |
| 4. #21422082 | C2 | semidirect |
| 5. C59×#2115 | C2 | semidirect |
| 6. C2×#14273749 | C4 | semidirect |
| 8. #16837660 | C4 | semidirect |
| 10. #16837655 | C4 | semidirect |
| 15. C2×#14273659 | C4 | semidirect |
| 167. #2115 | D59 | semidirect |
| 194. C59 | #11867 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21433758 | 2 |
| #21424142 | 2 |
| #21422085 | 2 |
| #21422082 | 2 |
| C59×#2115 | 2 |
| #11867 | 59 |