Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
438 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 438 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 3. #21422629 | C2 | semidirect |
| 4. #21422460 | C2 | semidirect |
| 5. #21422005 | C2 | semidirect |
| 6. #21421972 | C2 | semidirect |
| 27. C59×#484 | C4 | semidirect |
| 28. C59×#481 | C4 | semidirect |
| 32. C59×#451 | C4 | semidirect |
| 33. C59×#448 | C4 | semidirect |
| 227. #484 | Dic59 | semidirect |
| 228. #481 | Dic59 | semidirect |
| 232. #451 | Dic59 | semidirect |
| 233. #448 | Dic59 | semidirect |
| 251. C59 | #9331 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21433158 | 2 |
| #21422652 | 2 |
| #21422629 | 2 |
| #21422460 | 2 |
| #21422005 | 2 |
| #21421972 | 2 |
| C59×#3196 | 2 |
| #9331 | 59 |