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. #21437199 | C2 | semidirect |
| 3. #21425843 | C2 | semidirect |
| 4. C2×#16837214 | C2 | semidirect |
| 5. C59×#2916 | C2 | semidirect |
| 13. C2×#14273667 | C22 | semidirect |
| 14. #16837217 | C22 | semidirect |
| 15. #16837214 | C22 | semidirect |
| 19. C2×#108×C59 | C22 | semidirect |
| 114. #2916 | D59 | semidirect |
| 132. C2×#108 | 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 |
| #21437199 | 2 |
| #21425843 | 2 |
| C2×#16837214 | 2 |
| C59×#2916 | 2 |
| #33392 | 59 |