Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
464 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 464 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 |
|---|---|---|
| 2. #21424301 | C2 | semidirect |
| 3. #21424279 | C2 | semidirect |
| 5. #21421982 | C2 | semidirect |
| 6. #21421944 | C2 | semidirect |
| 22. #16837139 | C4 | semidirect |
| 23. #16837139 | C4 | semidirect |
| 24. #16837136 | C4 | semidirect |
| 25. #16837136 | C4 | semidirect |
| 248. C59 | #8874 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21433144 | 2 |
| #21424301 | 2 |
| #21424279 | 2 |
| #21422587 | 2 |
| #21421982 | 2 |
| #21421944 | 2 |
| C59×#1871 | 2 |
| #8874 | 59 |