Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
472 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 133 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. C22×Dic404 | C2 | semidirect |
| 2. C2×Q16×D101 | C2 | semidirect |
| 4. #20265555 | C2 | semidirect |
| 5. #20265419 | C2 | semidirect |
| 6. #20265386 | C2 | semidirect |
| 7. #20265334 | C2 | semidirect |
| 8. #20265332 | C2 | semidirect |
| 9. #20265271 | C2 | semidirect |
| 11. #467×C101 | C2 | semidirect |
| 55. Dic404 | D4 | semidirect |
| 90. C22⋊D101 | Q16 | semidirect |
| 112. C22×C101 | C2×Q16 | semidirect |
| 116. C2×D101 | C2×Q16 | semidirect |
| 126. Dic101 | C2×Q16 | semidirect |
| 133. C101 | D4×Q16 | semidirect |
| 139. #467 | D101 | semidirect |
| 248. C22 | Q16×D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Dic404 | 2 |
| C2×Q16×D101 | 2 |
| #20265840 | 2 |
| #20265555 | 2 |
| #20265419 | 2 |
| #20265386 | 2 |
| #20265334 | 2 |
| #20265332 | 2 |
| #20265271 | 2 |
| C8×C22⋊D101 | 2 |
| #467×C101 | 2 |
| D4×Q16 | 101 |