Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
670 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 670 conjugacy classes of subgroups — too many to draw. Only its 110 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C2×#99 |
| commutator | C22×C4 | C22×C4×C17 |
| Frattini, cosocle | C2×C4⋊C4 | C23×C17 |
| prime radical | C23×D4×C17 | C4 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C22×C4×C17 ◁ C2×C17×#117 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C17×#1464 | C2 | semidirect |
| 3. C17×#1318 | C2 | semidirect |
| 12. C17×#324 | C22 | semidirect |
| 69. #11509 | C17 | direct (N × H) |
| 105. #1464 | C2×C17 | semidirect |
| 106. #1318 | C2×C17 | semidirect |
| 136. #324 | C22×C17 | semidirect |
| 166. C17 | #11509 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C17×#2309 | 2 |
| C17×#1464 | 2 |
| C17×#1318 | 2 |
| #11509 | 17 |