Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
474 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 474 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 4. #21425012 | C2 | semidirect |
| 5. #21422204 | C2 | semidirect |
| 6. #21422184 | C2 | semidirect |
| 7. C2×C59×#358 | C2 | semidirect |
| 11. #16837843 | C4 | semidirect |
| 47. #14273667 | C2×C4 | semidirect |
| 64. C2×Q16×C59 | C2×C4 | semidirect |
| 179. C2×#358 | D59 | semidirect |
| 209. C59 | #13023 | semidirect |
| 222. C2×Q16 | C4×D59 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16837843 | 2 |
| #21432970 | 2 |
| C2×#16837210 | 2 |
| #21425012 | 2 |
| #21422204 | 2 |
| #21422184 | 2 |
| C2×C59×#358 | 2 |
| #13023 | 59 |