Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
618 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 618 conjugacy classes of subgroups — too many to draw. Only its 90 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×#15690875 | C2 | semidirect |
| 2. #20261706 | C2 | semidirect |
| 3. C4×C22⋊#87604 | C2 | semidirect |
| 5. C2×#13095521 | C22 | semidirect |
| 7. C2×C4×#87604 | C22 | semidirect |
| 15. C2×#13095512 | C4 | semidirect |
| 18. C22×D388 | C4 | semidirect |
| 21. C22×Q8×C97 | C4 | semidirect |
| 70. Q8×C97 | C22⋊C4 | semidirect |
| 83. D388 | C22⋊C4 | semidirect |
| 93. C22×C97 | #104 | semidirect |
| 120. C97 | #1789 | semidirect |
| 130. C22×Q8 | #87604 | semidirect |
| 187. Q8 | C22⋊#87604 | semidirect |
| 224. C22 | #15690875 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690875 | 2 |
| #20261706 | 2 |
| C4×C22⋊#87604 | 2 |
| C22×#13095512 | 2 |
| #1789 | 97 |