Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
318 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 318 conjugacy classes of subgroups — too many to draw. Only its 65 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. #21436520 | C2 | semidirect |
| 2. #21426319 | C2 | semidirect |
| 3. #21423448 | C2 | semidirect |
| 4. #21422153 | C2 | semidirect |
| 5. #21422057 | C2 | semidirect |
| 6. #21422050 | C2 | semidirect |
| 7. C59×#2206 | C2 | semidirect |
| 136. #2206 | D59 | semidirect |
| 164. C59 | #12343 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21436520 | 2 |
| #21426319 | 2 |
| #21423448 | 2 |
| #21422153 | 2 |
| #21422057 | 2 |
| #21422050 | 2 |
| C59×#2206 | 2 |
| #12343 | 59 |