Finite Group DatabasebetaFinite Group DatabasebetaOrder 23872.
124 conjugacy classes of subgroups; only the 48 normal subgroups are shown.
This group has 124 conjugacy classes of subgroups — too many to draw. Only its 48 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×#20238620 | C2 | semidirect |
| 2. C22×#15688419 | C2 | semidirect |
| 3. C4⋊#15688419 | C2 | semidirect |
| 4. #26045849 | C2 | semidirect |
| 5. C22⋊#15688419 | C2 | semidirect |
| 6. #26045847 | C2 | semidirect |
| 24. #15688419 | D4 | semidirect |
| 39. C22×C373 | M16 | semidirect |
| 55. C373 | #435 | semidirect |
| 98. C22 | #20238620 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20238620 | 2 |
| C22×#15688419 | 2 |
| C4⋊#15688419 | 2 |
| #26045849 | 2 |
| C22⋊#15688419 | 2 |
| #26045847 | 2 |
| #26045752 | 2 |
| #435 | 373 |