Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
580 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 580 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 4. #21424379 | C2 | semidirect |
| 5. #21424376 | C2 | semidirect |
| 6. #21422215 | C2 | semidirect |
| 7. C59×#1390 | C2 | semidirect |
| 21. #16837194 | C4 | semidirect |
| 54. #14273642 | C2×C4 | semidirect |
| 71. #99×C59 | C2×C4 | semidirect |
| 109. C2×D236 | C4⋊C4 | semidirect |
| 136. C4×Dic59 | C4⋊C4 | semidirect |
| 248. #1390 | D59 | semidirect |
| 279. C59 | #12966 | semidirect |
| 316. #99 | C4×D59 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21427271 | 2 |
| C2×#16837194 | 2 |
| #21424492 | 2 |
| #21424379 | 2 |
| #21424376 | 2 |
| #21422215 | 2 |
| C59×#1390 | 2 |
| #12966 | 59 |