Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
158 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 158 conjugacy classes of subgroups — too many to draw. Only its 53 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×#15690756 | C2 | semidirect |
| 4. C4⋊#13095486 | C2 | semidirect |
| 5. #20260538 | C2 | semidirect |
| 7. C4×Q16×C97 | C2 | semidirect |
| 73. C97 | #2211 | semidirect |
| 77. C4×Q16 | D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690756 | 2 |
| C2×#15690753 | 2 |
| #20261119 | 2 |
| C4⋊#13095486 | 2 |
| #20260538 | 2 |
| #20260535 | 2 |
| C4×Q16×C97 | 2 |
| #2211 | 97 |