Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
584 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 584 conjugacy classes of subgroups — too many to draw. Only its 171 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. C2×#16837440 | C2 | semidirect |
| 3. #21426305 | C2 | semidirect |
| 4. #21426288 | C2 | semidirect |
| 5. #21425884 | C2 | semidirect |
| 6. #21425809 | C2 | semidirect |
| 7. C59×#2112 | C2 | semidirect |
| 20. #16837230 | C22 | semidirect |
| 21. #16837228 | C22 | semidirect |
| 22. #16837207 | C22 | semidirect |
| 23. #16837204 | C22 | semidirect |
| 145. #2112 | D59 | semidirect |
| 170. C59 | #33647 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21433677 | 2 |
| C2×#16837440 | 2 |
| #21426305 | 2 |
| #21426288 | 2 |
| #21425884 | 2 |
| #21425809 | 2 |
| C59×#2112 | 2 |
| #33647 | 59 |