Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
750 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 750 conjugacy classes of subgroups — too many to draw. Only its 87 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. C2×#16837543 | C2 | semidirect |
| 3. C2×#16837540 | C2 | semidirect |
| 4. #21424019 | C2 | semidirect |
| 5. #21422457 | C2 | semidirect |
| 6. #21421984 | C2 | semidirect |
| 7. C59×#1471 | C2 | semidirect |
| 222. #1471 | D59 | semidirect |
| 255. C59 | #9988 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21434893 | 2 |
| C2×#16837543 | 2 |
| C2×#16837540 | 2 |
| #21424019 | 2 |
| #21422457 | 2 |
| #21421984 | 2 |
| C59×#1471 | 2 |
| #9988 | 59 |