Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
950 conjugacy classes of subgroups; only the 130 normal subgroups are shown.
This group has 950 conjugacy classes of subgroups — too many to draw. Only its 130 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 | #392 |
| commutator, Frattini, cosocle | C2×C42 | C23×C17 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C2×C42×C17 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C17×#3205 | C2 | semidirect |
| 2. C17×#2867 | C2 | semidirect |
| 3. C17×#1962 | C2 | semidirect |
| 4. C17×#1545 | C2 | semidirect |
| 5. C17×#1276 | C2 | semidirect |
| 26. C17×C4⋊Q8 | D4 | semidirect |
| 34. C17×#127 | D4 | semidirect |
| 42. C17×C4⋊C8 | D4 | semidirect |
| 78. C42×C17 | D8 | semidirect |
| 82. #10280 | C17 | direct (N × H) |
| 115. #3205 | C2×C17 | semidirect |
| 116. #2867 | C2×C17 | semidirect |
| 117. #1962 | C2×C17 | semidirect |
| 118. #1545 | C2×C17 | semidirect |
| 119. #1276 | C2×C17 | semidirect |
| 161. C4⋊Q8 | D4×C17 | semidirect |
| 169. #127 | D4×C17 | semidirect |
| 177. C4⋊C8 | D4×C17 | semidirect |
| 182. C17 | #10280 | direct (N × H) |
| 214. C42 | D8×C17 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C17×#3205 | 2 |
| C17×#2867 | 2 |
| C17×#1962 | 2 |
| C17×#1545 | 2 |
| C17×#1276 | 2 |
| #10280 | 17 |