Finite Group DatabasebetaFinite Group DatabasebetaOrder 1472.
290 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 290 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×#121 | C2 |
| hypercenter | #121 | D23 |
| hypocenter | C23 | #548 |
| 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. C2×#67290 | C2 | semidirect |
| 2. C22×Dic46 | C2 | semidirect |
| 3. C23×#121 | C2 | semidirect |
| 4. #10625110 | C2 | semidirect |
| 5. #10625107 | C2 | semidirect |
| 6. D4×Dic23 | C2 | semidirect |
| 7. C4×C22⋊D23 | C2 | semidirect |
| 8. #10625068 | C2 | semidirect |
| 9. #10625058 | C2 | semidirect |
| 10. #10625056 | C2 | semidirect |
| 11. #10625049 | C2 | semidirect |
| 58. Dic46 | D4 | semidirect |
| 64. C22×C23 | #41 | semidirect |
| 91. #121 | D23 | semidirect |
| 95. C23 | #548 | semidirect |
| 151. C22 | #67290 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#67290 | 2 |
| C22×Dic46 | 2 |
| C23×#121 | 2 |
| #10625110 | 2 |
| #10625107 | 2 |
| D4×Dic23 | 2 |
| C4×C22⋊D23 | 2 |
| #10625068 | 2 |
| #10625058 | 2 |
| #10625056 | 2 |
| #10625049 | 2 |
| #548 | 23 |