Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
938 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 938 conjugacy classes of subgroups — too many to draw. Only its 179 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. #21421984 | C2 | semidirect |
| 4. #21421983 | C2 | semidirect |
| 5. C59×#1298 | C2 | semidirect |
| 174. #1298 | D59 | direct (N × H) |
| 181. D59 | #1298 | direct (N × H) |
| 197. C59 | C2×#1298 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #407×D59 | 2 |
| C2×C22⋊C8×D59 | 2 |
| #21421984 | 2 |
| #21421983 | 2 |
| C59×#1298 | 2 |
| C2×#1298 | 59 |