Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
226 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 226 conjugacy classes of subgroups — too many to draw. Only its 53 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. #20265612 | C2 | semidirect |
| 2. #20265430 | C2 | semidirect |
| 3. #20264987 | C2 | semidirect |
| 4. #20264959 | C2 | semidirect |
| 5. #575×C101 | C2 | semidirect |
| 6. C2×D808 | C22 | semidirect |
| 10. #15692195 | C22 | semidirect |
| 11. #15692187 | C22 | semidirect |
| 35. Q16×C101 | D4 | semidirect |
| 39. D8×C101 | D4 | semidirect |
| 84. C101 | #2190 | semidirect |
| 85. #575 | D101 | semidirect |
| 115. Q16 | C22⋊D101 | semidirect |
| 120. D8 | C22⋊D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20265612 | 2 |
| #20265430 | 2 |
| #20264987 | 2 |
| #20264959 | 2 |
| #575×C101 | 2 |
| #2190 | 101 |