Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
226 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 226 conjugacy classes of subgroups — too many to draw. Only its 61 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×#15690753 | C2 | semidirect |
| 3. #20260539 | C2 | semidirect |
| 4. C22⋊#13095486 | C2 | semidirect |
| 5. C22×Q16×C97 | C2 | semidirect |
| 31. Q16×C97 | D4 | semidirect |
| 54. C22×C97 | SD32 | semidirect |
| 70. C97 | #2185 | semidirect |
| 71. C22×Q16 | D97 | semidirect |
| 97. Q16 | C22⋊D97 | semidirect |
| 127. C22 | #15690753 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690753 | 2 |
| #20260971 | 2 |
| #20260539 | 2 |
| C22⋊#13095486 | 2 |
| C22×Q16×C97 | 2 |
| #2185 | 97 |