Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
334 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 68 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. #20266170 | C2 | semidirect |
| 4. (C2×#87938)⋊Q8 | C2 | semidirect |
| 5. #20266056 | C2 | semidirect |
| 6. #20266049 | C2 | semidirect |
| 24. #15692288 | C4 | semidirect |
| 26. #15692286 | C4 | semidirect |
| 27. #15692285 | C4 | semidirect |
| 32. #137×C101 | C4 | semidirect |
| 56. C2×Dic202 | C2×C4 | semidirect |
| 73. #13108058 | C2×C4 | semidirect |
| 77. C2×Q8×C101 | C2×C4 | semidirect |
| 80. M16×C101 | C2×C4 | semidirect |
| 154. C101 | #1882 | semidirect |
| 169. #137 | #87938 | semidirect |
| 200. C2×Q8 | C2×#87938 | semidirect |
| 221. M16 | C2×#87938 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20266246 | 2 |
| D101⋊#104 | 2 |
| #20266170 | 2 |
| (C2×#87938)⋊Q8 | 2 |
| #20266056 | 2 |
| #20266049 | 2 |
| #137×D101 | 2 |
| #1882 | 101 |