Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
924 conjugacy classes of subgroups; only the 163 normal subgroups are shown.
This group has 924 conjugacy classes of subgroups — too many to draw. Only its 163 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. #21435479 | C2 | semidirect |
| 3. #21423377 | C2 | semidirect |
| 4. #21423328 | C2 | semidirect |
| 5. #21422834 | C2 | semidirect |
| 6. #21422548 | C2 | semidirect |
| 7. C59×#3160 | C2 | semidirect |
| 161. #3160 | D59 | semidirect |
| 193. C59 | #18701 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21438496 | 2 |
| #21435479 | 2 |
| #21423377 | 2 |
| #21423328 | 2 |
| #21422834 | 2 |
| #21422548 | 2 |
| C59×#3160 | 2 |
| #18701 | 59 |