Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
472 conjugacy classes of subgroups; only the 162 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 162 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×#15692343 | C2 | semidirect |
| 2. #20266221 | C2 | direct (N × H) |
| 3. C2×#15692326 | C2 | semidirect |
| 4. C2×#15692320 | C2 | semidirect |
| 5. C2×C8×#87938 | C2 | semidirect |
| 8. #15692343 | C22 | semidirect |
| 14. #15692326 | C22 | semidirect |
| 15. #15692320 | C22 | semidirect |
| 16. C8×#87938 | C22 | semidirect |
| 18. #15692278 | C4 | semidirect |
| 20. C2×#13108061 | C4 | semidirect |
| 21. C2×D808 | C4 | semidirect |
| 23. C2×Q16×C101 | C4 | semidirect |
| 44. #13108061 | C2×C4 | semidirect |
| 45. D808 | C2×C4 | semidirect |
| 50. Q16×C101 | C2×C4 | semidirect |
| 88. C2×C101 | #443 | semidirect |
| 94. C101 | C2×#443 | semidirect |
| 104. C2×Q16 | #87938 | semidirect |
| 128. Q16 | C2×#87938 | semidirect |
| 185. C2 | #20266221 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15692343 | 2 |
| #20266221 | 2 |
| C2×#15692326 | 2 |
| C2×#15692320 | 2 |
| C2×C8×#87938 | 2 |
| C2×#15692278 | 2 |
| C2×#443 | 101 |