Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
336 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 59 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. D4×D404 | C2 | semidirect |
| 2. #20265553 | C2 | semidirect |
| 3. #20265369 | C2 | semidirect |
| 4. #20264920 | C2 | semidirect |
| 5. D4⋊#11717579 | C2 | semidirect |
| 6. #20264904 | C2 | semidirect |
| 7. #459×C101 | C2 | semidirect |
| 17. C4⋊#11717579 | C22 | semidirect |
| 19. C4×#11717579 | C22 | semidirect |
| 21. #127×C101 | C22 | semidirect |
| 23. C4⋊C8×C101 | C22 | semidirect |
| 67. D4×C101 | D8 | semidirect |
| 83. D404 | D8 | semidirect |
| 118. C101 | #1619 | semidirect |
| 122. #459 | D101 | semidirect |
| 132. #127 | C2×D101 | semidirect |
| 139. C4⋊C8 | C2×D101 | semidirect |
| 194. D4 | #13108059 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×D404 | 2 |
| #20265553 | 2 |
| #20265369 | 2 |
| #20264920 | 2 |
| D4⋊#11717579 | 2 |
| #20264904 | 2 |
| #459×C101 | 2 |
| #1619 | 101 |