Finite Group DatabasebetaFinite Group DatabasebetaOrder 1472.
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×D23 |
| commutator, socle, cosocle | C22×C23 | C24 |
| Fitting | C23×#117 | C2 |
| hypercenter | #117 | D23 |
| hypocenter | C23 | #553 |
| LCS | G ▷ C22×C23 ▷ C23 | |
| UCS | C1 ◁ C22 ◁ #117 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C23×#117 | C2 | semidirect |
| 2. #10625101 | C2 | semidirect |
| 3. C4×C22⋊D23 | C2 | semidirect |
| 4. #10625066 | C2 | semidirect |
| 5. #10625064 | C2 | semidirect |
| 6. C4⋊C4×D23 | C2 | semidirect |
| 7. #10625061 | C2 | semidirect |
| 8. #10625055 | C2 | semidirect |
| 9. #10625054 | C2 | semidirect |
| 10. #10625047 | C2 | semidirect |
| 11. C4×D92 | C2 | semidirect |
| 88. #117 | D23 | semidirect |
| 90. C23 | #553 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#117 | 2 |
| #10625101 | 2 |
| C4×C22⋊D23 | 2 |
| #10625066 | 2 |
| #10625064 | 2 |
| C4⋊C4×D23 | 2 |
| #10625061 | 2 |
| #10625055 | 2 |
| #10625054 | 2 |
| #10625047 | 2 |
| C4×D92 | 2 |
| #553 | 23 |