Finite Group DatabasebetaFinite Group DatabasebetaOrder 1472.
290 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 290 conjugacy classes of subgroups — too many to draw. Only its 105 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×#124 | C2 |
| hypercenter | #124 | D23 |
| hypocenter | C23 | #548 |
| LCS | G ▷ C22×C23 ▷ C23 | |
| UCS | C1 ◁ C22 ◁ #124 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×Q8×D23 | C2 | semidirect |
| 2. C2×#67290 | C2 | semidirect |
| 3. C23×#124 | C2 | semidirect |
| 4. #10625117 | C2 | semidirect |
| 5. #10625109 | C2 | semidirect |
| 6. #10625056 | C2 | semidirect |
| 7. #10625055 | C2 | semidirect |
| 8. (C22⋊D23)⋊C4 | C2 | semidirect |
| 9. #10625049 | C2 | semidirect |
| 10. C4×D92 | C2 | semidirect |
| 11. C4×Dic46 | C2 | semidirect |
| 58. Dic46 | D4 | semidirect |
| 68. C2×D23 | #41 | semidirect |
| 87. #124 | D23 | semidirect |
| 95. C23 | #548 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×D23 | 2 |
| C2×#67290 | 2 |
| C23×#124 | 2 |
| #10625117 | 2 |
| #10625109 | 2 |
| #10625056 | 2 |
| #10625055 | 2 |
| (C22⋊D23)⋊C4 | 2 |
| #10625049 | 2 |
| C4×D92 | 2 |
| C4×Dic46 | 2 |
| #548 | 23 |