Finite Group DatabasebetaFinite Group DatabasebetaOrder 23488.
238 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 238 conjugacy classes of subgroups — too many to draw. Only its 97 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D367 |
| commutator, socle, cosocle | C22×C367 | C24 |
| Fitting | C4×D4×C367 | C2 |
| hypercenter | C4×D4 | D367 |
| hypocenter | C367 | #553 |
| LCS | G ▷ C22×C367 ▷ C367 | |
| UCS | C1 ◁ C22 ◁ C4×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #26044255 | C2 | semidirect |
| 2. #26044254 | C2 | semidirect |
| 3. #26044251 | C2 | semidirect |
| 4. #26044246 | C2 | semidirect |
| 5. #26044244 | C2 | semidirect |
| 6. #26044235 | C2 | semidirect |
| 7. #26044234 | C2 | semidirect |
| 8. #26044233 | C2 | semidirect |
| 9. #26044233 | C2 | semidirect |
| 10. C4×C22⋊D367 | C2 | semidirect |
| 11. (C22⋊D367)⋊C4 | C2 | semidirect |
| 12. (C22⋊D367)⋊C4 | C2 | semidirect |
| 13. #26044218 | C2 | semidirect |
| 14. C2×Dic367⋊C4 | C2 | semidirect |
| 15. C4×D4×C367 | C2 | semidirect |
| 109. C367 | #553 | semidirect |
| 123. C4×D4 | D367 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26044255 | 2 |
| #26044254 | 2 |
| #26044251 | 2 |
| #26044246 | 2 |
| #26044244 | 2 |
| #26044235 | 2 |
| #26044234 | 2 |
| #26044233 | 2 |
| C4×C22⋊D367 | 2 |
| (C22⋊D367)⋊C4 | 2 |
| #26044218 | 2 |
| C2×Dic367⋊C4 | 2 |
| C4×D4×C367 | 2 |
| #553 | 367 |