Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
394 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 394 conjugacy classes of subgroups — too many to draw. Only its 92 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 | #120 |
| commutator, Frattini, cosocle | C22×C4 | C23×C17 |
| prime radical | C17×#535 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C22×C4×C17 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C17×#137 | C2 | semidirect |
| 3. C2×C17×#124 | C2 | semidirect |
| 4. C2×C17×#104 | C2 | semidirect |
| 5. C17×#419 | C2 | semidirect |
| 6. C2×C17×#100 | C2 | semidirect |
| 7. C17×#339 | C2 | semidirect |
| 40. C2×Q8×C17 | D4 | semidirect |
| 59. M16×C17 | D4 | semidirect |
| 68. C42×C17 | D4 | semidirect |
| 107. #2004 | C17 | direct (N × H) |
| 126. C2×#137 | C2×C17 | semidirect |
| 128. C2×#124 | C2×C17 | semidirect |
| 129. C2×#104 | C2×C17 | semidirect |
| 130. #419 | C2×C17 | semidirect |
| 131. C2×#100 | C2×C17 | semidirect |
| 132. #339 | C2×C17 | semidirect |
| 160. C17 | #2004 | direct (N × H) |
| 172. C2×Q8 | D4×C17 | semidirect |
| 191. M16 | D4×C17 | semidirect |
| 200. C42 | D4×C17 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C17×#137 | 2 |
| C17×#535 | 2 |
| C2×C17×#124 | 2 |
| C2×C17×#104 | 2 |
| C17×#419 | 2 |
| C2×C17×#100 | 2 |
| C17×#339 | 2 |
| #2004 | 17 |