Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
612 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 612 conjugacy classes of subgroups — too many to draw. Only its 94 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×#15692318 | C2 | semidirect |
| 2. C2×#15692317 | C2 | semidirect |
| 3. D101⋊(C22⋊C8) | C2 | semidirect |
| 4. #20266119 | C2 | semidirect |
| 14. C2×#13108075 | C4 | semidirect |
| 16. C2×#13108074 | C4 | semidirect |
| 18. C2×#13108073 | C4 | semidirect |
| 26. C2×#41×C101 | C4 | semidirect |
| 92. Q8×C101 | C22⋊C4 | semidirect |
| 95. D4×C101 | C22⋊C4 | semidirect |
| 112. D404 | C22⋊C4 | semidirect |
| 124. Dic202 | C22⋊C4 | semidirect |
| 165. C101 | #1788 | semidirect |
| 178. C2×#41 | #87938 | semidirect |
| 257. Q8 | C22⋊#87938 | semidirect |
| 266. D4 | C22⋊#87938 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15692318 | 2 |
| C2×#15692317 | 2 |
| D101⋊(C22⋊C8) | 2 |
| #20266119 | 2 |
| C2×#41×D101 | 2 |
| #1788 | 101 |