Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
568 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 568 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. #21437232 | C2 | semidirect |
| 2. C2×#16837840 | C2 | semidirect |
| 3. #21434582 | C2 | semidirect |
| 4. #21425833 | C2 | semidirect |
| 5. #21425813 | C2 | semidirect |
| 6. #21424994 | C2 | semidirect |
| 7. C59×#1378 | C2 | semidirect |
| 47. C2×Dic236 | D4 | semidirect |
| 59. C2×D472 | D4 | semidirect |
| 81. M32×C59 | D4 | semidirect |
| 83. C2×C16×C59 | D4 | semidirect |
| 217. #1378 | D59 | semidirect |
| 250. C59 | #13334 | semidirect |
| 295. M32 | D236 | semidirect |
| 297. C2×C16 | D236 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21437232 | 2 |
| C2×#16837840 | 2 |
| #21434582 | 2 |
| #21425833 | 2 |
| #21425813 | 2 |
| #21424994 | 2 |
| C59×#1378 | 2 |
| #13334 | 59 |