Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
1026 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 1026 conjugacy classes of subgroups — too many to draw. Only its 119 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. #21422789 | C2 | semidirect |
| 3. #21422706 | C2 | semidirect |
| 4. #21422437 | C2 | semidirect |
| 5. C59×#1955 | C2 | semidirect |
| 14. #16837459 | C22 | semidirect |
| 20. C2×C4⋊C8×C59 | C22 | semidirect |
| 22. C2×#97×C59 | C22 | semidirect |
| 164. #1955 | D59 | semidirect |
| 184. C2×C4⋊C8 | C2×D59 | semidirect |
| 186. C2×#97 | C2×D59 | semidirect |
| 191. C59 | #8456 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21437860 | 2 |
| #21422789 | 2 |
| #21422706 | 2 |
| #21422437 | 2 |
| C59×#1955 | 2 |
| #8456 | 59 |