Finite Group DatabasebetaFinite Group DatabasebetaOrder 20032.
152 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 39 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. #23756528 | C2 | semidirect |
| 3. #23756486 | C2 | semidirect |
| 4. #23756424 | C2 | semidirect |
| 5. #23756423 | C2 | semidirect |
| 6. #23756413 | C2 | semidirect |
| 7. #137×C313 | C2 | semidirect |
| 17. #19097545 | C22 | semidirect |
| 19. C4×Dic313 | C22 | semidirect |
| 21. C2×Q8×C313 | C22 | semidirect |
| 24. M16×C313 | C22 | semidirect |
| 64. C313 | #455 | semidirect |
| 68. #137 | D313 | semidirect |
| 77. C2×Q8 | C2×D313 | semidirect |
| 87. M16 | C2×D313 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23756543 | 2 |
| #23756528 | 2 |
| #23756486 | 2 |
| #23756424 | 2 |
| #23756423 | 2 |
| #23756413 | 2 |
| #137×C313 | 2 |
| #455 | 313 |