Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
540 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 540 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 1. C22×#14273672 | C2 | semidirect |
| 3. #21433752 | C2 | semidirect |
| 4. C2×#16837217 | C2 | semidirect |
| 5. #21425811 | C2 | semidirect |
| 6. C2×#16837185 | C2 | semidirect |
| 7. C59×#1382 | C2 | semidirect |
| 194. #1382 | D59 | semidirect |
| 222. C59 | #13320 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14273672 | 2 |
| C2×#16837673 | 2 |
| #21433752 | 2 |
| C2×#16837217 | 2 |
| #21425811 | 2 |
| C2×#16837185 | 2 |
| C59×#1382 | 2 |
| #13320 | 59 |