Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
336 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 94 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. C2×#15692324 | C2 | semidirect |
| 3. #20266051 | C2 | semidirect |
| 10. C22×#11717579 | C4 | semidirect |
| 12. C2×C8×D101 | C4 | semidirect |
| 13. C2×C8×D101 | C4 | semidirect |
| 16. C22×C8×C101 | C4 | semidirect |
| 64. C8×C101 | C22⋊C4 | semidirect |
| 66. #11717579 | C22⋊C4 | semidirect |
| 69. C22×C101 | #107 | semidirect |
| 75. C2×D101 | #107 | semidirect |
| 94. C101 | #1808 | semidirect |
| 106. C22×C8 | #87938 | semidirect |
| 160. C8 | C22⋊#87938 | semidirect |
| 172. C22 | #15692324 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15692324 | 2 |
| #20266119 | 2 |
| #20266051 | 2 |
| C22×C8×D101 | 2 |
| #1808 | 101 |