Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
466 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 111 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×#16837216 | C2 | semidirect |
| 3. #21425833 | C2 | semidirect |
| 4. #21425825 | C2 | semidirect |
| 5. #21425813 | C2 | semidirect |
| 6. #21424220 | C2 | semidirect |
| 7. C59×#2110 | C2 | semidirect |
| 13. #16837786 | C4 | semidirect |
| 14. #16837779 | C4 | semidirect |
| 62. M32×C59 | D4 | semidirect |
| 64. C2×C16×C59 | D4 | semidirect |
| 174. #2110 | D59 | semidirect |
| 201. C59 | #13215 | semidirect |
| 233. M32 | D236 | semidirect |
| 235. C2×C16 | D236 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21434582 | 2 |
| C2×#16837216 | 2 |
| #21425833 | 2 |
| #21425825 | 2 |
| #21425813 | 2 |
| #21424220 | 2 |
| C59×#2110 | 2 |
| #13215 | 59 |