Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
338 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 71 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 |
|---|---|---|
| 1. D8×Dic118 | C2 | semidirect |
| 2. #21426320 | C2 | semidirect |
| 4. #21423457 | C2 | semidirect |
| 5. #21422152 | C2 | semidirect |
| 6. #21422076 | C2 | semidirect |
| 7. C59×#1331 | C2 | semidirect |
| 65. D8×C59 | SD16 | semidirect |
| 109. Dic118 | D16 | semidirect |
| 138. #1331 | D59 | semidirect |
| 161. C59 | #12352 | semidirect |
| 206. D8 | #11745660 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D8×Dic118 | 2 |
| #21426320 | 2 |
| #21426131 | 2 |
| #21423457 | 2 |
| #21422152 | 2 |
| #21422076 | 2 |
| C59×#1331 | 2 |
| #12352 | 59 |