Finite Group DatabasebetaFinite Group DatabasebetaOrder 2944.
184 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 97 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 |
|---|---|---|
| 3. C4⋊(C23⋊C16) | C2 | semidirect |
| 4. Dic23⋊C16 | C2 | semidirect |
| 5. C23×C4⋊C16 | C2 | semidirect |
| 40. C4×D23 | C16 | semidirect |
| 54. C4×C23 | C2×C16 | semidirect |
| 59. Dic23 | C2×C16 | semidirect |
| 64. C4⋊C16 | D23 | direct (N × H) |
| 68. D23 | C4⋊C16 | direct (N × H) |
| 79. C23 | C2×C4⋊C16 | semidirect |
| 120. C4 | C16×D23 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C16×D23 | 2 |
| C4×C8×D23 | 2 |
| C4⋊(C23⋊C16) | 2 |
| Dic23⋊C16 | 2 |
| C23×C4⋊C16 | 2 |
| C2×C4⋊C16 | 23 |