Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
554 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 554 conjugacy classes of subgroups — too many to draw. Only its 94 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C17 | #120 |
| commutator, Frattini, cosocle | C2×C42 | C23×C17 |
| prime radical | C17×#2011 | C2 |
| LCS | G ▷ C2×C42 ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C17 ◁ C2×C42×C17 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C17×#2808 | C2 | semidirect |
| 2. C17×#2041 | C2 | semidirect |
| 3. C17×#2014 | C2 | semidirect |
| 5. C17×#1272 | C2 | semidirect |
| 6. C17×#1271 | C2 | semidirect |
| 7. C17×#1270 | C2 | semidirect |
| 129. #7746 | C17 | direct (N × H) |
| 191. #2808 | C2×C17 | semidirect |
| 192. #2041 | C2×C17 | semidirect |
| 193. #2014 | C2×C17 | semidirect |
| 195. #1272 | C2×C17 | semidirect |
| 196. #1271 | C2×C17 | semidirect |
| 197. #1270 | C2×C17 | semidirect |
| 296. C17 | #7746 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C17×#2808 | 2 |
| C17×#2041 | 2 |
| C17×#2014 | 2 |
| C17×#2011 | 2 |
| C17×#1272 | 2 |
| C17×#1271 | 2 |
| C17×#1270 | 2 |
| #7746 | 17 |