Finite Group DatabasebetaFinite Group DatabasebetaOrder 23872.
238 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 238 conjugacy classes of subgroups — too many to draw. Only its 61 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×#20238589 | C2 | semidirect |
| 3. C2×C22⋊Dic373 | C2 | semidirect |
| 4. C2×#20238587 | C2 | semidirect |
| 5. C2×#20238587 | C2 | semidirect |
| 6. #26045699 | C2 | semidirect |
| 7. C2×C22⋊C4×C373 | C2 | semidirect |
| 39. C2×Dic373 | D4 | semidirect |
| 89. C373 | #394 | semidirect |
| 96. C2×C22⋊C4 | D373 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C22⋊D373 | 2 |
| C2×#20238589 | 2 |
| C2×C22⋊Dic373 | 2 |
| C2×#20238587 | 2 |
| #26045699 | 2 |
| C2×C22⋊C4×C373 | 2 |
| #394 | 373 |