Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
558 conjugacy classes of subgroups; only the 360 normal subgroups are shown.
This group has 558 conjugacy classes of subgroups — too many to draw. Only its 360 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C4×C8 | #595 |
| commutator, hypocenter | C17 | C42×C16 |
| Frattini | C22×C4 | C22×#595 |
| Fitting | C2×C4×C8×C17 | C4 |
| socle, prime radical | C23×C17 | C22×C8 |
| cosocle | C22×#3622 | C23 |
| LCS | G ▷ C17 | |
| UCS | C1 ◁ C2×C4×C8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 5. #11763695 | C4 | direct (N × H) |
| 6. C4×#63216 | C4 | semidirect |
| 32. C4×Dic17 | C16 | semidirect |
| 39. #63216 | C42 | semidirect |
| 59. C4×C17 | C4×C16 | semidirect |
| 63. Dic17 | C4×C16 | semidirect |
| 87. C17 | C42×C16 | semidirect |
| 120. C4 | #11763695 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11763695 | 2 |
| C2×C4×#63216 | 2 |
| C4×C8×Dic17 | 2 |
| C42×C16 | 17 |