Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
164 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 164 conjugacy classes of subgroups — too many to draw. Only its 66 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×#15692330 | C2 | semidirect |
| 2. C22×#13108077 | C2 | semidirect |
| 3. #20266098 | C2 | semidirect |
| 4. #20266072 | C2 | semidirect |
| 5. C22⋊#13108077 | C2 | semidirect |
| 6. #20266066 | C2 | semidirect |
| 24. #13108077 | D4 | semidirect |
| 59. C22×C101 | M32 | semidirect |
| 76. C101 | #2168 | semidirect |
| 138. C22 | #15692330 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15692330 | 2 |
| C22×#13108077 | 2 |
| #20266098 | 2 |
| #20266072 | 2 |
| C22⋊#13108077 | 2 |
| #20266066 | 2 |
| #20265240 | 2 |
| #2168 | 101 |