Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
726 conjugacy classes of subgroups; only the 200 normal subgroups are shown.
This group has 726 conjugacy classes of subgroups — too many to draw. Only its 200 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. D101⋊#131 | C2 | semidirect |
| 2. #20266246 | C2 | semidirect |
| 3. #20266170 | C2 | semidirect |
| 4. #20266168 | C2 | semidirect |
| 5. #20266167 | C2 | semidirect |
| 6. C2×#15692318 | C2 | semidirect |
| 22. #15692303 | C4 | semidirect |
| 24. #15692302 | C4 | semidirect |
| 25. #15692302 | C4 | semidirect |
| 31. 2−1+4×C101 | C4 | semidirect |
| 45. #13108075 | C2×C4 | semidirect |
| 51. #13108074 | C2×C4 | semidirect |
| 55. #13108073 | C2×C4 | semidirect |
| 59. C2×Dic202 | C2×C4 | semidirect |
| 64. Q8×D101 | C2×C4 | semidirect |
| 75. #41×C101 | C2×C4 | semidirect |
| 77. C2×Q8×C101 | C2×C4 | semidirect |
| 142. C101 | #2898 | semidirect |
| 155. 2−1+4 | #87938 | semidirect |
| 189. #41 | C2×#87938 | semidirect |
| 201. C2×Q8 | C2×#87938 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D101⋊#131 | 2 |
| #20266246 | 2 |
| #20266170 | 2 |
| #20266168 | 2 |
| #20266167 | 2 |
| C2×#15692318 | 2 |
| 2−1+4×D101 | 2 |
| #2898 | 101 |