Finite Group DatabasebetaFinite Group DatabasebetaOrder 23488.
258 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 77 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. C2×Dic367⋊C4 | C2 | semidirect |
| 3. C2×C22⋊Dic367 | C2 | semidirect |
| 4. C2×(C2×D367)⋊C4 | C2 | semidirect |
| 5. C2×(C2×D367)⋊C4 | C2 | semidirect |
| 6. C2×C4×Dic367 | C2 | semidirect |
| 7. C2×C22⋊C4×C367 | C2 | semidirect |
| 11. C2×C22⋊D367 | C4 | semidirect |
| 40. C2×Dic367 | D4 | semidirect |
| 54. C2×C4×C367 | D4 | semidirect |
| 80. Dic367 | C22⋊C4 | semidirect |
| 90. C367 | #390 | semidirect |
| 97. C2×C22⋊C4 | D367 | semidirect |
| 145. C2×C4 | C22⋊D367 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C22⋊D367 | 2 |
| C2×Dic367⋊C4 | 2 |
| C2×C22⋊Dic367 | 2 |
| C2×(C2×D367)⋊C4 | 2 |
| C2×C4×Dic367 | 2 |
| C2×C22⋊C4×C367 | 2 |
| #390 | 367 |