Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
260 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 88 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 | #99 |
| commutator | C2×C4 | C22×C4×C17 |
| Frattini, cosocle | C2×Q8 | C23×C17 |
| prime radical | C22×D4×C17 | C4 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C23×C17 ◁ C22×Q8×C17 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C17×#101 | C2 | semidirect |
| 3. C17×#355 | C2 | direct (N × H) |
| 13. C17×#101 | C22 | semidirect |
| 55. C2×#355 | C17 | direct (N × H) |
| 70. C2×#101 | C2×C17 | semidirect |
| 71. #355 | C2×C17 | direct (N × H) |
| 75. C2×C17 | #355 | direct (N × H) |
| 86. #101 | C22×C17 | semidirect |
| 87. C17 | C2×#355 | direct (N × H) |
| 145. C2 | C17×#355 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C17×#124 | 2 |
| C2×C17×#101 | 2 |
| C17×#355 | 2 |
| C2×#355 | 17 |