Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
368 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 117 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×#15692278 | C2 | semidirect |
| 2. C2×#15692274 | C2 | semidirect |
| 3. #20265608 | C2 | direct (N × H) |
| 4. C2×#15692201 | C2 | semidirect |
| 5. C2×#15692200 | C2 | semidirect |
| 6. C2×#15692196 | C2 | semidirect |
| 7. C2×C16×D101 | C2 | semidirect |
| 8. C2×SD32×C101 | C2 | semidirect |
| 12. #15692278 | C22 | semidirect |
| 14. #15692274 | C22 | semidirect |
| 20. #15692201 | C22 | semidirect |
| 21. #15692200 | C22 | semidirect |
| 22. #15692196 | C22 | semidirect |
| 24. C16×D101 | C22 | semidirect |
| 27. SD32×C101 | C22 | semidirect |
| 95. C2×C101 | #508 | semidirect |
| 100. C101 | C2×#508 | semidirect |
| 106. C2×SD32 | D101 | semidirect |
| 124. SD32 | C2×D101 | semidirect |
| 197. C2 | #20265608 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15692278 | 2 |
| C2×#15692274 | 2 |
| #20265608 | 2 |
| C2×#15692201 | 2 |
| C2×#15692200 | 2 |
| C2×#15692196 | 2 |
| C2×C16×D101 | 2 |
| C2×SD32×C101 | 2 |
| C2×#508 | 101 |