Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
1154 conjugacy classes of subgroups; only the 351 normal subgroups are shown.
This group has 1154 conjugacy classes of subgroups — too many to draw. Only its 351 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. #21432707 | C2 | semidirect |
| 3. #21425846 | C2 | semidirect |
| 4. C2×#16837216 | C2 | semidirect |
| 5. C59×#3407 | C2 | semidirect |
| 14. C2×#14273663 | C22 | semidirect |
| 15. #16837219 | C22 | semidirect |
| 16. #16837216 | C22 | semidirect |
| 19. C2×M32×C59 | C22 | semidirect |
| 113. #3407 | D59 | semidirect |
| 130. C2×M32 | C2×D59 | semidirect |
| 135. C59 | #33392 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16838207 | 2 |
| #21432707 | 2 |
| #21425846 | 2 |
| C2×#16837216 | 2 |
| C59×#3407 | 2 |
| #33392 | 59 |