Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
774 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 774 conjugacy classes of subgroups — too many to draw. Only its 111 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. #21424931 | C2 | semidirect |
| 3. #21424040 | C2 | semidirect |
| 4. #21422611 | C2 | semidirect |
| 5. #21422002 | C2 | semidirect |
| 6. #21421982 | C2 | semidirect |
| 7. C59×#2341 | C2 | semidirect |
| 8. C2×#14273752 | C4 | semidirect |
| 14. #16837403 | C4 | semidirect |
| 155. Q8×C59 | #99 | semidirect |
| 230. #2341 | D59 | semidirect |
| 266. C59 | #9368 | semidirect |
| 393. Q8 | #14273641 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21433348 | 2 |
| #21424931 | 2 |
| #21424040 | 2 |
| #21422611 | 2 |
| #21422002 | 2 |
| #21421982 | 2 |
| C59×#2341 | 2 |
| #9368 | 59 |