Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
532 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 101 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 |
|---|---|---|
| 1. C2×#16837843 | C2 | semidirect |
| 3. C2×#16837208 | C2 | semidirect |
| 4. C2×#16837206 | C2 | semidirect |
| 5. C2×#16837186 | C2 | semidirect |
| 6. #21422206 | C2 | semidirect |
| 7. C2×C59×#473 | C2 | semidirect |
| 48. #14273667 | D4 | semidirect |
| 67. C2×Q16×C59 | D4 | semidirect |
| 79. #108×C59 | D4 | semidirect |
| 206. C2×#473 | D59 | semidirect |
| 242. C59 | #13308 | semidirect |
| 259. C2×Q16 | C22⋊D59 | semidirect |
| 287. #108 | C22⋊D59 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16837843 | 2 |
| #21433766 | 2 |
| C2×#16837208 | 2 |
| C2×#16837206 | 2 |
| C2×#16837186 | 2 |
| #21422206 | 2 |
| C2×C59×#473 | 2 |
| #13308 | 59 |