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×#121 | C2 |
| hypercenter | #121 | D23 |
| hypocenter | C23 | #553 |
| LCS | G ▷ C22×C23 ▷ C23 | |
| UCS | C1 ◁ C22 ◁ #121 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C23×#121 | C2 | semidirect |
| 2. #10625109 | C2 | semidirect |
| 3. #10625109 | C2 | semidirect |
| 4. #10625106 | C2 | semidirect |
| 5. D4×Dic23 | C2 | semidirect |
| 6. C4×C22⋊D23 | C2 | semidirect |
| 7. #10625097 | C2 | semidirect |
| 8. C4⋊C4×D23 | C2 | semidirect |
| 9. #10625061 | C2 | semidirect |
| 10. (C22⋊D23)⋊C4 | C2 | semidirect |
| 11. #10625050 | C2 | semidirect |
| 84. #121 | 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×#121 | 2 |
| #10625109 | 2 |
| #10625106 | 2 |
| D4×Dic23 | 2 |
| C4×C22⋊D23 | 2 |
| #10625097 | 2 |
| C4⋊C4×D23 | 2 |
| #10625061 | 2 |
| (C22⋊D23)⋊C4 | 2 |
| #10625050 | 2 |
| #553 | 23 |