Finite Group DatabasebetaFinite Group DatabasebetaOrder 2944.
492 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 157 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. #13092672 | C2 | direct (N × H) |
| 4. C2×#10624999 | C2 | semidirect |
| 5. C2×#10625017 | C2 | semidirect |
| 6. C22×Q16×C23 | C2 | semidirect |
| 10. C2×Q16×C23 | C22 | semidirect |
| 20. #10625017 | C22 | semidirect |
| 21. #10624999 | C22 | semidirect |
| 80. C22×Q16 | D23 | semidirect |
| 86. C2×C23 | #470 | semidirect |
| 93. C2×Q16 | C2×D23 | semidirect |
| 105. C23 | C2×#470 | semidirect |
| 164. C2 | #13092672 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#67262 | 2 |
| C2×#10625117 | 2 |
| #13092672 | 2 |
| C2×#10624999 | 2 |
| C2×#10625017 | 2 |
| C22×Q16×C23 | 2 |
| C2×#470 | 23 |