Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
738 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 738 conjugacy classes of subgroups — too many to draw. Only its 157 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. C23×Dic202 | C2 | semidirect |
| 2. C2×#15692288 | C2 | semidirect |
| 4. #20265335 | C2 | semidirect |
| 5. #20265318 | C2 | semidirect |
| 6. #20265187 | C2 | semidirect |
| 7. #407×C101 | C2 | semidirect |
| 16. C2×Dic404 | C22 | semidirect |
| 17. C2×#13108063 | C22 | semidirect |
| 24. #15692180 | C22 | semidirect |
| 35. C2×Dic202 | D4 | semidirect |
| 93. C22×C101 | #137 | semidirect |
| 109. C101 | #3004 | semidirect |
| 116. #407 | D101 | semidirect |
| 204. C22 | #15692288 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×Dic202 | 2 |
| C2×#15692288 | 2 |
| #20265688 | 2 |
| #20265335 | 2 |
| #20265318 | 2 |
| #20265187 | 2 |
| #407×C101 | 2 |
| #3004 | 101 |