Finite Group DatabasebetaFinite Group DatabasebetaOrder 2944.
174 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 174 conjugacy classes of subgroups — too many to draw. Only its 81 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×C16×D23 | C2 | semidirect |
| 3. Dic23⋊C16 | C2 | semidirect |
| 4. C22⋊(C23⋊C16) | C2 | semidirect |
| 5. (C2×D23)⋊C16 | C2 | semidirect |
| 6. C16×Dic23 | C2 | semidirect |
| 7. C22×C16×C23 | C2 | semidirect |
| 37. C16×C23 | D4 | semidirect |
| 46. C22⋊D23 | C16 | direct (N × H) |
| 60. C22×C23 | C2×C16 | semidirect |
| 64. C2×D23 | C2×C16 | semidirect |
| 70. Dic23 | C2×C16 | semidirect |
| 72. C22×C16 | D23 | semidirect |
| 96. C23 | D4×C16 | semidirect |
| 115. C16 | C22⋊D23 | direct (N × H) |
| 138. C22 | 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 |
| C8×C22⋊D23 | 2 |
| Dic23⋊C16 | 2 |
| C22⋊(C23⋊C16) | 2 |
| (C2×D23)⋊C16 | 2 |
| C16×Dic23 | 2 |
| C22×C16×C23 | 2 |
| D4×C16 | 23 |