Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
558 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 558 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. #21432815 | C2 | semidirect |
| 3. #21422764 | C2 | semidirect |
| 4. #21422655 | C2 | semidirect |
| 5. #21421954 | C2 | semidirect |
| 6. #21421927 | C2 | semidirect |
| 7. C59×#1961 | C2 | semidirect |
| 10. #16837778 | C4 | semidirect |
| 11. #16837748 | C4 | semidirect |
| 100. C2×C8×C59 | D8 | semidirect |
| 191. #1961 | D59 | semidirect |
| 222. C59 | #9293 | semidirect |
| 304. C2×C8 | #11745669 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21435014 | 2 |
| #21432815 | 2 |
| #21422764 | 2 |
| #21422655 | 2 |
| #21421954 | 2 |
| #21421927 | 2 |
| C59×#1961 | 2 |
| #9293 | 59 |