Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
362 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 79 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. #20265651 | C2 | semidirect |
| 3. #20265194 | C2 | semidirect |
| 4. C2×#15692171 | C2 | semidirect |
| 5. #20264934 | C2 | semidirect |
| 6. #20264933 | C2 | semidirect |
| 7. #421×C101 | C2 | semidirect |
| 10. #15692251 | C4 | semidirect |
| 11. #15692244 | C4 | semidirect |
| 43. C4×Dic101 | C2×C4 | semidirect |
| 44. C4×Dic101 | D4 | semidirect |
| 49. C2×Q8×C101 | C2×C4 | semidirect |
| 51. C2×D4×C101 | C2×C4 | semidirect |
| 59. C42×C101 | D4 | semidirect |
| 117. C101 | #1911 | semidirect |
| 121. #421 | D101 | semidirect |
| 147. C2×Q8 | C4×D101 | semidirect |
| 156. C2×D4 | C4×D101 | semidirect |
| 176. C42 | C22⋊D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20265741 | 2 |
| #20265651 | 2 |
| #20265194 | 2 |
| C2×#15692171 | 2 |
| #20264934 | 2 |
| #20264933 | 2 |
| #421×C101 | 2 |
| #1911 | 101 |