Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
246 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 246 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. #21426352 | C2 | semidirect |
| 2. #21423461 | C2 | semidirect |
| 4. #21422168 | C2 | semidirect |
| 5. #21422146 | C2 | semidirect |
| 6. #21422143 | C2 | semidirect |
| 7. C59×#2169 | C2 | semidirect |
| 73. C16×C59 | D8 | semidirect |
| 114. #2169 | D59 | semidirect |
| 140. C59 | #12435 | semidirect |
| 191. C16 | #11745669 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21426352 | 2 |
| #21423461 | 2 |
| #21423451 | 2 |
| #21422168 | 2 |
| #21422146 | 2 |
| #21422143 | 2 |
| C59×#2169 | 2 |
| #12435 | 59 |