Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
346 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 346 conjugacy classes of subgroups — too many to draw. Only its 67 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. #21436443 | C2 | semidirect |
| 2. #21426321 | C2 | semidirect |
| 3. #21426132 | C2 | semidirect |
| 4. #21423452 | C2 | semidirect |
| 5. #21422056 | C2 | semidirect |
| 6. #21422050 | C2 | semidirect |
| 7. C59×#1364 | C2 | semidirect |
| 108. D236 | D16 | semidirect |
| 142. #1364 | D59 | semidirect |
| 168. C59 | #12340 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21436443 | 2 |
| #21426321 | 2 |
| #21426132 | 2 |
| #21423452 | 2 |
| #21422056 | 2 |
| #21422050 | 2 |
| C59×#1364 | 2 |
| #12340 | 59 |