Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
766 conjugacy classes of subgroups; only the 161 normal subgroups are shown.
This group has 766 conjugacy classes of subgroups — too many to draw. Only its 161 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. #20265684 | C2 | semidirect |
| 2. #20265367 | C2 | semidirect |
| 3. #20265364 | C2 | semidirect |
| 4. #20265151 | C2 | semidirect |
| 5. #585×C101 | C2 | semidirect |
| 6. C22×C4×D101 | C22 | semidirect |
| 7. #15692236 | C22 | semidirect |
| 10. #15692223 | C22 | semidirect |
| 12. #15692214 | C22 | semidirect |
| 13. #15692170 | C22 | semidirect |
| 36. C2×Q8×C101 | D4 | semidirect |
| 39. C2×D4×C101 | D4 | semidirect |
| 42. C22×C4×C101 | D4 | semidirect |
| 83. C101 | #3025 | semidirect |
| 84. #585 | D101 | semidirect |
| 109. C2×Q8 | C22⋊D101 | semidirect |
| 113. C2×D4 | C22⋊D101 | semidirect |
| 119. C22×C4 | C22⋊D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20265684 | 2 |
| #20265367 | 2 |
| #20265364 | 2 |
| #20265151 | 2 |
| #585×C101 | 2 |
| #3025 | 101 |