Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
302 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 302 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 |
|---|---|---|
| 2. #20266188 | C2 | semidirect |
| 4. #20266123 | C2 | semidirect |
| 5. #20266056 | C2 | semidirect |
| 6. #20266048 | C2 | semidirect |
| 25. #15692183 | C4 | semidirect |
| 26. #15692182 | C4 | semidirect |
| 27. #15692181 | C4 | semidirect |
| 28. #104×C101 | C4 | semidirect |
| 58. #13108058 | C2×C4 | semidirect |
| 62. C4×Dic101 | C2×C4 | semidirect |
| 64. M16×C101 | C2×C4 | semidirect |
| 65. C42×C101 | C2×C4 | semidirect |
| 75. Q8×C101 | C4⋊C4 | semidirect |
| 77. D4×C101 | C4⋊C4 | semidirect |
| 88. D404 | C4⋊C4 | semidirect |
| 99. Dic202 | C4⋊C4 | semidirect |
| 132. C101 | #1859 | semidirect |
| 158. #104 | #87938 | semidirect |
| 180. M16 | C2×#87938 | semidirect |
| 197. C42 | C2×#87938 | semidirect |
| 202. Q8 | C4⋊#87938 | semidirect |
| 209. D4 | C4⋊#87938 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20266246 | 2 |
| #20266188 | 2 |
| #20266168 | 2 |
| #20266123 | 2 |
| #20266056 | 2 |
| #20266048 | 2 |
| #104×D101 | 2 |
| #1859 | 101 |