Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
344 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 344 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 |
|---|---|---|
| 1. #20265943 | C2 | semidirect |
| 3. #20265182 | C2 | semidirect |
| 4. #20265150 | C2 | semidirect |
| 5. #20264934 | C2 | semidirect |
| 6. #20264933 | C2 | semidirect |
| 7. #418×C101 | C2 | semidirect |
| 13. #15692251 | C4 | semidirect |
| 14. #15692242 | C4 | semidirect |
| 37. C2×#11717579 | D4 | semidirect |
| 56. C2×C8×C101 | D4 | semidirect |
| 116. C101 | #1910 | semidirect |
| 120. #418 | D101 | semidirect |
| 165. C2×C8 | C22⋊D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20265943 | 2 |
| #20265744 | 2 |
| #20265182 | 2 |
| #20265150 | 2 |
| #20264934 | 2 |
| #20264933 | 2 |
| #418×C101 | 2 |
| #1910 | 101 |