Finite Group DatabasebetaFinite Group DatabasebetaOrder 23488.
128 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 128 conjugacy classes of subgroups — too many to draw. Only its 43 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×#19154564 | C2 | semidirect |
| 3. Q8×Dic367 | C2 | semidirect |
| 4. Dic367⋊C8 | C2 | semidirect |
| 5. #26044183 | C2 | semidirect |
| 6. #26044182 | C2 | semidirect |
| 7. C2×SD16×C367 | C2 | semidirect |
| 32. Q8×C367 | D4 | semidirect |
| 50. Dic367 | SD16 | semidirect |
| 56. C367 | #460 | semidirect |
| 59. C2×SD16 | D367 | semidirect |
| 81. Q8 | C22⋊D367 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19154564 | 2 |
| #26044257 | 2 |
| Q8×Dic367 | 2 |
| Dic367⋊C8 | 2 |
| #26044183 | 2 |
| #26044182 | 2 |
| C2×SD16×C367 | 2 |
| #460 | 367 |