Finite Group DatabasebetaFinite Group DatabasebetaOrder 1472.
292 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 292 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×C4⋊Q8 | C2 |
| hypercenter | C4⋊Q8 | D23 |
| hypocenter | C23 | #547 |
| LCS | G ▷ C22×C23 ▷ C23 | |
| UCS | C1 ◁ C22 ◁ C4⋊Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#67292 | C2 | semidirect |
| 2. C23×C4⋊Q8 | C2 | semidirect |
| 3. #10625117 | C2 | semidirect |
| 4. #10625066 | C2 | semidirect |
| 5. #10625065 | C2 | semidirect |
| 6. C4⋊C4×D23 | C2 | semidirect |
| 7. C4×D92 | C2 | semidirect |
| 8. C4×D92 | C2 | semidirect |
| 37. D92 | D4 | semidirect |
| 51. C4×C23 | #41 | semidirect |
| 61. C4⋊Q8 | D23 | semidirect |
| 68. C23 | #547 | semidirect |
| 113. C4 | #67292 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#67292 | 2 |
| C23×C4⋊Q8 | 2 |
| #10625117 | 2 |
| #10625066 | 2 |
| #10625065 | 2 |
| C4⋊C4×D23 | 2 |
| C4×D92 | 2 |
| #547 | 23 |