Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
544 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 544 conjugacy classes of subgroups — too many to draw. Only its 109 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. #21432815 | C2 | semidirect |
| 3. #21422746 | C2 | semidirect |
| 4. #21422521 | C2 | semidirect |
| 5. #21421993 | C2 | semidirect |
| 6. #21421941 | C2 | semidirect |
| 7. C59×#1955 | C2 | semidirect |
| 105. C2×C8×C59 | D8 | semidirect |
| 203. #1955 | D59 | semidirect |
| 236. C59 | #9049 | semidirect |
| 321. C2×C8 | #11745669 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21434096 | 2 |
| #21432815 | 2 |
| #21422746 | 2 |
| #21422521 | 2 |
| #21421993 | 2 |
| #21421941 | 2 |
| C59×#1955 | 2 |
| #9049 | 59 |