Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
812 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 812 conjugacy classes of subgroups — too many to draw. Only its 107 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. #21424024 | C2 | semidirect |
| 3. #21422422 | C2 | semidirect |
| 4. #21422005 | C2 | semidirect |
| 5. C59×#2879 | C2 | semidirect |
| 68. C22⋊C8×C59 | D4 | semidirect |
| 242. #2879 | D59 | semidirect |
| 275. C59 | #9511 | semidirect |
| 315. C22⋊C8 | C22⋊D59 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21427411 | 2 |
| #21424024 | 2 |
| #21422422 | 2 |
| #21422005 | 2 |
| C59×#2879 | 2 |
| #9511 | 59 |