Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
472 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 133 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×#10597388 | C2 | semidirect |
| 3. #11926923 | C2 | semidirect |
| 4. #11926800 | C2 | semidirect |
| 5. #11926754 | C2 | semidirect |
| 6. #11926746 | C2 | semidirect |
| 7. #11926704 | C2 | semidirect |
| 8. #11926700 | C2 | semidirect |
| 9. C4×#64527 | C2 | semidirect |
| 10. #11926622 | C2 | semidirect |
| 11. D4×Q8×C19 | C2 | semidirect |
| 72. #64527 | D4 | semidirect |
| 125. C4×C19 | #137 | semidirect |
| 131. D4×Q8 | D19 | semidirect |
| 176. C19 | #3276 | semidirect |
| 261. C4 | #10597388 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10597388 | 2 |
| #11927199 | 2 |
| #11926923 | 2 |
| #11926800 | 2 |
| #11926754 | 2 |
| #11926746 | 2 |
| #11926704 | 2 |
| #11926700 | 2 |
| C4×#64527 | 2 |
| #11926622 | 2 |
| D4×Q8×C19 | 2 |
| #3276 | 19 |