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. C2×#16837239 | C2 | semidirect |
| 4. #21422285 | C2 | semidirect |
| 5. #21422279 | C2 | semidirect |
| 6. #21422238 | C2 | semidirect |
| 7. C59×#2222 | C2 | semidirect |
| 18. #16837236 | C22 | semidirect |
| 19. C2×C59⋊C32 | C22 | semidirect |
| 20. C2×Q32×C59 | C22 | semidirect |
| 23. C59×#368 | C22 | semidirect |
| 118. #2222 | D59 | semidirect |
| 132. C2×Q32 | C2×D59 | semidirect |
| 142. #368 | C2×D59 | semidirect |
| 144. C59 | #13671 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21437237 | 2 |
| #21426414 | 2 |
| C2×#16837239 | 2 |
| #21422285 | 2 |
| #21422279 | 2 |
| #21422238 | 2 |
| C59×#2222 | 2 |
| #13671 | 59 |