Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
422 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 87 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. #21425868 | C2 | semidirect |
| 3. C2×#16837216 | C2 | semidirect |
| 4. #21425811 | C2 | semidirect |
| 5. #21425725 | C2 | semidirect |
| 6. #21424147 | C2 | semidirect |
| 7. C59×#1384 | C2 | semidirect |
| 47. C2×C59⋊C16 | D4 | semidirect |
| 166. #1384 | D59 | semidirect |
| 190. C59 | #13396 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21433745 | 2 |
| #21425868 | 2 |
| C2×#16837216 | 2 |
| #21425811 | 2 |
| #21425725 | 2 |
| #21424147 | 2 |
| C59×#1384 | 2 |
| #13396 | 59 |