Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
1244 conjugacy classes of subgroups; only the 199 normal subgroups are shown.
This group has 1244 conjugacy classes of subgroups — too many to draw. Only its 199 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. C4×#14273708 | C2 | semidirect |
| 2. #21425448 | C2 | semidirect |
| 3. #21425344 | C2 | semidirect |
| 4. #21425262 | C2 | semidirect |
| 5. #21425225 | C2 | semidirect |
| 6. C4×#14273642 | C2 | semidirect |
| 98. C22×Dic59 | #41 | semidirect |
| 114. C22⋊Dic59 | #41 | semidirect |
| 216. C59 | #23596 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14273708 | 2 |
| #21425448 | 2 |
| #21425344 | 2 |
| #21425262 | 2 |
| #21425225 | 2 |
| C4×#14273642 | 2 |
| C59×#3459 | 2 |
| #23596 | 59 |