Finite Group DatabasebetaFinite Group DatabasebetaOrder 1472.
238 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 238 conjugacy classes of subgroups — too many to draw. Only its 99 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 | C4×D4×C23 | C2 |
| hypercenter | C4×D4 | D23 |
| hypocenter | C23 | #553 |
| LCS | G ▷ C22×C23 ▷ C23 | |
| UCS | C1 ◁ C22 ◁ C4×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C4×D4×C23 | C2 | semidirect |
| 2. #10625110 | C2 | semidirect |
| 3. #10625101 | C2 | semidirect |
| 4. #10625101 | C2 | semidirect |
| 5. #10625097 | C2 | semidirect |
| 6. C2×C4⋊Dic23 | C2 | semidirect |
| 7. #10625069 | C2 | semidirect |
| 8. #10625054 | C2 | semidirect |
| 9. (C22⋊D23)⋊C4 | C2 | semidirect |
| 10. C4×D92 | C2 | semidirect |
| 11. #10625041 | C2 | semidirect |
| 87. C4×D4 | D23 | semidirect |
| 90. C23 | #553 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×D4×C23 | 2 |
| #10625110 | 2 |
| #10625101 | 2 |
| #10625097 | 2 |
| C2×C4⋊Dic23 | 2 |
| #10625069 | 2 |
| #10625054 | 2 |
| (C22⋊D23)⋊C4 | 2 |
| C4×D92 | 2 |
| #10625041 | 2 |
| #553 | 23 |