Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
472 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 141 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×Q16×D19 | C2 | semidirect |
| 3. #11926924 | C2 | semidirect |
| 4. #11926786 | C2 | semidirect |
| 5. #11926754 | C2 | semidirect |
| 6. #11926701 | C2 | semidirect |
| 8. C4×Q16×C19 | C2 | semidirect |
| 37. Q16×C19 | D4 | semidirect |
| 65. D76 | Q16 | direct (N × H) |
| 79. C2×D19 | C2×Q16 | semidirect |
| 83. C4×C19 | C2×Q16 | semidirect |
| 94. C4×Q16 | D19 | semidirect |
| 120. C19 | D4×Q16 | semidirect |
| 132. Q16 | D76 | direct (N × H) |
| 176. C4 | Q16×D19 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q16×D19 | 2 |
| Q8×D76 | 2 |
| #11926924 | 2 |
| #11926786 | 2 |
| #11926754 | 2 |
| #11926701 | 2 |
| C8×D76 | 2 |
| C4×Q16×C19 | 2 |
| D4×Q16 | 19 |