Finite Group DatabasebetaFinite Group DatabasebetaOrder 1472.
294 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 294 conjugacy classes of subgroups — too many to draw. Only its 103 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×C22⋊Q8 | C2 |
| hypercenter | C22⋊Q8 | D23 |
| hypocenter | C23 | #537 |
| LCS | G ▷ C22×C23 ▷ C23 | |
| UCS | C1 ◁ C22 ◁ C22⋊Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#67292 | C2 | semidirect |
| 2. C2×#67288 | C2 | semidirect |
| 3. C23×C22⋊Q8 | C2 | semidirect |
| 4. #10625117 | C2 | semidirect |
| 5. #10625101 | C2 | semidirect |
| 6. #10625067 | C2 | semidirect |
| 7. #10625066 | C2 | semidirect |
| 8. #10625066 | C2 | semidirect |
| 9. C4⋊C4×D23 | C2 | semidirect |
| 10. #10625055 | C2 | semidirect |
| 11. #10625055 | C2 | semidirect |
| 60. C4×D23 | D4 | semidirect |
| 94. C22⋊Q8 | D23 | semidirect |
| 101. C23 | #537 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#67292 | 2 |
| C2×#67288 | 2 |
| C23×C22⋊Q8 | 2 |
| #10625117 | 2 |
| #10625101 | 2 |
| #10625067 | 2 |
| #10625066 | 2 |
| C4⋊C4×D23 | 2 |
| #10625055 | 2 |
| #537 | 23 |