Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
492 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 492 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. #21432688 | C2 | semidirect |
| 3. C2×#16837212 | C2 | semidirect |
| 4. #21425725 | C2 | semidirect |
| 5. #21422212 | C2 | semidirect |
| 6. #21422195 | C2 | semidirect |
| 7. C59×#2145 | C2 | semidirect |
| 12. #16837674 | C4 | semidirect |
| 13. #16837669 | C4 | semidirect |
| 53. #14273663 | C2×C4 | semidirect |
| 65. C2×Q16×C59 | C2×C4 | semidirect |
| 67. C2×D8×C59 | C2×C4 | semidirect |
| 190. #2145 | D59 | semidirect |
| 222. C59 | #13005 | semidirect |
| 234. C2×Q16 | C4×D59 | semidirect |
| 236. C2×D8 | C4×D59 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21433812 | 2 |
| #21432688 | 2 |
| C2×#16837212 | 2 |
| #21425725 | 2 |
| #21422212 | 2 |
| #21422195 | 2 |
| C59×#2145 | 2 |
| #13005 | 59 |