Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
234 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 73 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. #21422981 | C2 | semidirect |
| 3. #21422980 | C2 | semidirect |
| 4. #21422169 | C2 | semidirect |
| 5. #21422058 | C2 | semidirect |
| 6. #21422012 | C2 | semidirect |
| 7. C59×#1331 | C2 | semidirect |
| 68. C59⋊C16 | M16 | semidirect |
| 112. #1331 | D59 | semidirect |
| 134. C59 | #12086 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14273668 | 2 |
| #21422981 | 2 |
| #21422980 | 2 |
| #21422169 | 2 |
| #21422058 | 2 |
| #21422012 | 2 |
| C59×#1331 | 2 |
| #12086 | 59 |