Finite Group DatabasebetaFinite Group DatabasebetaOrder 1472.
312 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 107 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×#127 | C2 |
| hypercenter | #127 | D23 |
| hypocenter | C23 | #550 |
| LCS | G ▷ C22×C23 ▷ C23 | |
| UCS | C1 ◁ C22 ◁ #127 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#67290 | C2 | semidirect |
| 2. C23×#127 | C2 | semidirect |
| 3. #10625111 | C2 | semidirect |
| 4. #10625110 | C2 | semidirect |
| 5. #10625109 | C2 | semidirect |
| 6. D4×Dic23 | C2 | semidirect |
| 7. C4×D92 | C2 | semidirect |
| 8. C4×Dic46 | C2 | semidirect |
| 42. Dic46 | D4 | semidirect |
| 52. C4×C23 | #41 | semidirect |
| 64. #127 | D23 | semidirect |
| 70. C23 | #550 | semidirect |
| 117. C4 | #67290 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#67290 | 2 |
| C23×#127 | 2 |
| #10625111 | 2 |
| #10625110 | 2 |
| #10625109 | 2 |
| D4×Dic23 | 2 |
| C4×D92 | 2 |
| C4×Dic46 | 2 |
| #550 | 23 |