Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
174 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 174 conjugacy classes of subgroups — too many to draw. Only its 57 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. C4⋊#13095486 | C2 | semidirect |
| 4. #20260535 | C2 | semidirect |
| 5. C4×Q16×C97 | C2 | semidirect |
| 25. Q16×C97 | D4 | semidirect |
| 54. C4×C97 | SD32 | semidirect |
| 62. C97 | #2207 | semidirect |
| 65. C4×Q16 | D97 | semidirect |
| 83. Q16 | D388 | semidirect |
| 116. C4 | #15690753 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690753 | 2 |
| #20261112 | 2 |
| C4⋊#13095486 | 2 |
| #20260535 | 2 |
| C4×Q16×C97 | 2 |
| #2207 | 97 |