Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
702 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 702 conjugacy classes of subgroups — too many to draw. Only its 111 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. C2×#16837198 | C2 | semidirect |
| 3. #21424020 | C2 | semidirect |
| 4. #21422222 | C2 | semidirect |
| 5. C22×#101×C59 | C2 | semidirect |
| 71. #101×C59 | D4 | semidirect |
| 206. C22×C59 | #355 | semidirect |
| 225. C22×#101 | D59 | semidirect |
| 257. C59 | #13092 | semidirect |
| 297. #101 | C22⋊D59 | semidirect |
| 443. C22 | #16837198 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21427750 | 2 |
| C2×#16837198 | 2 |
| #21424020 | 2 |
| #21422222 | 2 |
| C22×#101×C59 | 2 |
| #13092 | 59 |