Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
544 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 544 conjugacy classes of subgroups — too many to draw. Only its 173 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 |
|---|---|---|
| 3. #20265379 | C2 | direct (N × H) |
| 4. C2×C4⋊#11717579 | C2 | semidirect |
| 5. C2×#15692179 | C2 | semidirect |
| 6. C2×C4⋊Q8×C101 | C2 | semidirect |
| 16. C4⋊#11717579 | C22 | semidirect |
| 17. #15692179 | C22 | semidirect |
| 20. C4⋊Q8×C101 | C22 | semidirect |
| 61. C2×C4×C101 | SD16 | semidirect |
| 86. C4×C101 | C2×SD16 | semidirect |
| 90. C2×C101 | #461 | semidirect |
| 96. C101 | C2×#461 | semidirect |
| 98. C2×C4⋊Q8 | D101 | semidirect |
| 110. C4⋊Q8 | C2×D101 | semidirect |
| 163. C2×C4 | #13108061 | semidirect |
| 183. C4 | C2×#13108061 | semidirect |
| 187. C2 | #20265379 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13108061 | 2 |
| C2×C4×D404 | 2 |
| #20265379 | 2 |
| C2×C4⋊#11717579 | 2 |
| C2×#15692179 | 2 |
| C2×C4⋊Q8×C101 | 2 |
| C2×#461 | 101 |