Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
552 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 153 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×#15692288 | C2 | semidirect |
| 2. C2×#15692286 | C2 | semidirect |
| 3. C2×#15692285 | C2 | semidirect |
| 5. C2×#15692253 | C2 | semidirect |
| 6. #20265570 | C2 | semidirect |
| 7. #20265568 | C2 | semidirect |
| 8. #20265555 | C2 | semidirect |
| 9. #20265548 | C2 | semidirect |
| 10. M16×Dic101 | C2 | semidirect |
| 11. C2×#137×C101 | C2 | semidirect |
| 62. #13108058 | D4 | semidirect |
| 86. M16×C101 | D4 | semidirect |
| 140. Dic101 | #137 | semidirect |
| 147. C101 | #3152 | semidirect |
| 151. C2×#137 | D101 | semidirect |
| 224. M16 | C22⋊D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15692288 | 2 |
| C2×#15692286 | 2 |
| C2×#15692285 | 2 |
| #20265723 | 2 |
| C2×#15692253 | 2 |
| #20265570 | 2 |
| #20265568 | 2 |
| #20265555 | 2 |
| #20265548 | 2 |
| M16×Dic101 | 2 |
| C2×#137×C101 | 2 |
| #3152 | 101 |