Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
318 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 318 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. C2×#16837180 | C2 | semidirect |
| 3. #21422130 | C2 | semidirect |
| 4. #21422128 | C2 | semidirect |
| 5. C2×C59×#347 | C2 | semidirect |
| 136. C2×#347 | D59 | semidirect |
| 161. C59 | #11911 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21434442 | 2 |
| C2×#16837180 | 2 |
| #21422130 | 2 |
| #21422128 | 2 |
| C2×C59×#347 | 2 |
| #11911 | 59 |