Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
504 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 131 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. C2×#15692278 | C2 | semidirect |
| 2. #20265846 | C2 | semidirect |
| 3. #20265552 | C2 | semidirect |
| 4. #20265413 | C2 | semidirect |
| 5. #20265410 | C2 | semidirect |
| 6. #20265375 | C2 | semidirect |
| 7. #20265322 | C2 | semidirect |
| 8. #20265321 | C2 | semidirect |
| 9. Q16×Dic101 | C2 | semidirect |
| 10. C8×C22⋊D101 | C2 | semidirect |
| 11. C2×#135×C101 | C2 | semidirect |
| 74. Q16×C101 | D4 | semidirect |
| 134. Dic101 | #135 | semidirect |
| 143. C101 | #3287 | semidirect |
| 145. C2×#135 | D101 | semidirect |
| 202. Q16 | C22⋊D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15692278 | 2 |
| #20265846 | 2 |
| #20265552 | 2 |
| #20265413 | 2 |
| #20265410 | 2 |
| #20265375 | 2 |
| #20265322 | 2 |
| #20265321 | 2 |
| Q16×Dic101 | 2 |
| C8×C22⋊D101 | 2 |
| C2×#135×C101 | 2 |
| #3287 | 101 |