Finite Group DatabasebetaFinite Group DatabasebetaOrder 26368.
632 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 632 conjugacy classes of subgroups — too many to draw. Only its 106 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C103 | #99 |
| commutator | C22×C4 | C22×C4×C103 |
| Frattini, cosocle | C2×C4⋊C4 | C23×C103 |
| socle | C22×C103 | C2×#99 |
| prime radical | C103×#2388 | C2 |
| LCS | G ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C103 ◁ C22×C4×C103 ◁ C2×C4×D4×C103 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C4×#100×C103 | C2 | semidirect |
| 3. C103×#1459 | C2 | semidirect |
| 4. C103×#1354 | C2 | semidirect |
| 5. C103×#1345 | C2 | semidirect |
| 199. #11733 | C103 | direct (N × H) |
| 209. C4×#100 | C2×C103 | semidirect |
| 210. #1459 | C2×C103 | semidirect |
| 211. #1354 | C2×C103 | semidirect |
| 212. #1345 | C2×C103 | semidirect |
| 213. C103 | #11733 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C103×#2388 | 2 |
| C4×#100×C103 | 2 |
| C103×#1459 | 2 |
| C103×#1354 | 2 |
| C103×#1345 | 2 |
| #11733 | 103 |