Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
418 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 115 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. #21422844 | C2 | semidirect |
| 4. #21421954 | C2 | semidirect |
| 5. C59×#1835 | C2 | semidirect |
| 9. #16837481 | C4 | semidirect |
| 11. C8×D236 | C4 | semidirect |
| 131. #1835 | D59 | semidirect |
| 156. C59 | #8678 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21432809 | 2 |
| #21422844 | 2 |
| #21422655 | 2 |
| #21421954 | 2 |
| C59×#1835 | 2 |
| #8678 | 59 |