Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
350 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 350 conjugacy classes of subgroups — too many to draw. Only its 103 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. #21422859 | C2 | semidirect |
| 3. #21422153 | C2 | semidirect |
| 4. #21422143 | C2 | semidirect |
| 5. C2×C59×C4⋊C16 | C2 | semidirect |
| 120. C2×C4⋊C16 | D59 | semidirect |
| 144. C59 | #11982 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21434675 | 2 |
| #21422859 | 2 |
| #21422153 | 2 |
| #21422143 | 2 |
| C2×C59×C4⋊C16 | 2 |
| #11982 | 59 |