Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
356 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 356 conjugacy classes of subgroups — too many to draw. Only its 113 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. #20265899 | C2 | semidirect |
| 2. #20265570 | C2 | semidirect |
| 4. #20265399 | C2 | semidirect |
| 6. #20265386 | C2 | semidirect |
| 7. #20265307 | C2 | semidirect |
| 8. #20265276 | C2 | semidirect |
| 9. C4×Q16×C101 | C2 | semidirect |
| 103. C101 | #3402 | semidirect |
| 112. C4×Q16 | D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20265899 | 2 |
| #20265570 | 2 |
| #20265561 | 2 |
| #20265399 | 2 |
| #20265395 | 2 |
| #20265386 | 2 |
| #20265307 | 2 |
| #20265276 | 2 |
| C4×Q16×C101 | 2 |
| #3402 | 101 |