Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
376 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 109 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⋊C8×Dic59 | C2 | semidirect |
| 3. #21422871 | C2 | semidirect |
| 5. #21421993 | C2 | semidirect |
| 6. #21421928 | C2 | semidirect |
| 21. C59×#332 | C4 | semidirect |
| 22. C59×#331 | C4 | semidirect |
| 175. #332 | Dic59 | semidirect |
| 176. #331 | Dic59 | semidirect |
| 178. C59 | #9577 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21424925 | 2 |
| C4⋊C8×Dic59 | 2 |
| #21422871 | 2 |
| #21422495 | 2 |
| #21421993 | 2 |
| #21421928 | 2 |
| C59×#1540 | 2 |
| #9577 | 59 |