Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
552 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 141 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×#15692287 | C2 | semidirect |
| 2. C2×#15692284 | C2 | semidirect |
| 4. C4⋊Q8×D101 | C2 | semidirect |
| 5. #20265572 | C2 | semidirect |
| 6. #20265571 | C2 | semidirect |
| 7. #20265569 | C2 | semidirect |
| 8. #20265555 | C2 | semidirect |
| 9. #20265548 | C2 | semidirect |
| 10. #20265129 | C2 | semidirect |
| 11. #497×C101 | C2 | semidirect |
| 63. #13108057 | D4 | semidirect |
| 124. Dic101 | #137 | semidirect |
| 131. C101 | #3152 | semidirect |
| 139. #497 | D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15692287 | 2 |
| C2×#15692284 | 2 |
| #20265726 | 2 |
| C4⋊Q8×D101 | 2 |
| #20265572 | 2 |
| #20265571 | 2 |
| #20265569 | 2 |
| #20265555 | 2 |
| #20265548 | 2 |
| #20265129 | 2 |
| #497×C101 | 2 |
| #3152 | 101 |