Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
622 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 622 conjugacy classes of subgroups — too many to draw. Only its 99 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. #21433568 | C2 | semidirect |
| 3. #21429001 | C2 | semidirect |
| 4. #21422657 | C2 | semidirect |
| 5. #21422522 | C2 | semidirect |
| 6. #21421955 | C2 | semidirect |
| 7. C59×#1479 | C2 | semidirect |
| 92. C2×Q8×C59 | D8 | semidirect |
| 242. #1479 | D59 | semidirect |
| 276. C59 | #9997 | semidirect |
| 341. C2×Q8 | D472 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21434097 | 2 |
| #21433568 | 2 |
| #21429001 | 2 |
| #21422657 | 2 |
| #21422522 | 2 |
| #21421955 | 2 |
| C59×#1479 | 2 |
| #9997 | 59 |