Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
780 conjugacy classes of subgroups; only the 140 normal subgroups are shown.
This group has 780 conjugacy classes of subgroups — too many to draw. Only its 140 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. C22×C4⋊#87604 | C2 | semidirect |
| 3. C2×(C2×#87604)⋊C4 | C2 | semidirect |
| 4. C2×(C2×#87604)⋊C4 | C2 | semidirect |
| 18. C2×C22⋊Dic97 | C4 | semidirect |
| 19. C2×#13095488 | C4 | semidirect |
| 20. C2×#13095488 | C4 | semidirect |
| 23. C2×C22⋊C4×C97 | C4 | semidirect |
| 73. C23×C97 | C4⋊C4 | semidirect |
| 97. C22×D97 | C4⋊C4 | semidirect |
| 125. C2×C4×C97 | C22⋊C4 | semidirect |
| 129. C2×Dic97 | C22⋊C4 | semidirect |
| 195. C97 | #1439 | semidirect |
| 216. C2×C22⋊C4 | #87604 | semidirect |
| 301. C23 | C4⋊#87604 | semidirect |
| 330. C2×C4 | C22⋊#87604 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4⋊#87604 | 2 |
| C22×C22⋊#87604 | 2 |
| C2×(C2×#87604)⋊C4 | 2 |
| C2×C22⋊C4×D97 | 2 |
| #1439 | 97 |