Finite Group DatabasebetaFinite Group DatabasebetaOrder 2944.
272 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 117 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 |
|---|---|---|
| 2. C22×C23⋊C16 | C2 | semidirect |
| 3. (C2×D23)⋊C16 | C2 | direct (N × H) |
| 4. C22×C16×C23 | C2 | semidirect |
| 13. C2×C16×C23 | C22 | semidirect |
| 15. C2×C23⋊C16 | C22 | semidirect |
| 37. C22×D23 | C16 | semidirect |
| 60. C2×D23 | C2×C16 | semidirect |
| 67. C22×C16 | D23 | semidirect |
| 69. C2×C23 | C22⋊C16 | semidirect |
| 84. C2×C16 | C2×D23 | semidirect |
| 85. C23 | C2×C22⋊C16 | semidirect |
| 135. C2 | (C2×D23)⋊C16 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C8×D23 | 2 |
| C22×C23⋊C16 | 2 |
| (C2×D23)⋊C16 | 2 |
| C22×C16×C23 | 2 |
| C2×C22⋊C16 | 23 |