Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
890 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 890 conjugacy classes of subgroups — too many to draw. Only its 135 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. #21425831 | C2 | semidirect |
| 3. #21425801 | C2 | semidirect |
| 4. #21425710 | C2 | semidirect |
| 5. C59×#1812 | C2 | semidirect |
| 11. #16838202 | C4 | semidirect |
| 14. C2×#14273667 | C22 | semidirect |
| 15. C22×C59⋊C16 | C22 | semidirect |
| 21. C59×#427 | C22 | semidirect |
| 167. #1812 | D59 | semidirect |
| 184. #427 | C2×D59 | semidirect |
| 191. C59 | #12745 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21438870 | 2 |
| #21425831 | 2 |
| #21425801 | 2 |
| #21425710 | 2 |
| C59×#1812 | 2 |
| #12745 | 59 |