Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
284 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 59 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. #21426414 | C2 | semidirect |
| 3. #21422282 | C2 | semidirect |
| 4. #21422236 | C2 | semidirect |
| 5. C59×#2219 | C2 | semidirect |
| 13. #16837236 | C22 | semidirect |
| 14. C2×Q32×C59 | C22 | semidirect |
| 17. C59×#367 | C22 | semidirect |
| 106. #2219 | D59 | semidirect |
| 118. C2×Q32 | C2×D59 | semidirect |
| 124. #367 | C2×D59 | semidirect |
| 126. C59 | #13668 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21437232 | 2 |
| #21426414 | 2 |
| #21422282 | 2 |
| #21422236 | 2 |
| C59×#2219 | 2 |
| #13668 | 59 |