Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
394 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 394 conjugacy classes of subgroups — too many to draw. Only its 101 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 |
|---|---|---|
| 3. #21422038 | C2 | semidirect |
| 4. #21422037 | C2 | semidirect |
| 5. C59×#1323 | C2 | semidirect |
| 123. #1323 | D59 | direct (N × H) |
| 128. D59 | #1323 | direct (N × H) |
| 142. C59 | C2×#1323 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #424×D59 | 2 |
| C22⋊C16×D59 | 2 |
| #21422038 | 2 |
| #21422037 | 2 |
| C59×#1323 | 2 |
| C2×#1323 | 59 |